The Belgian opened the scoring after just three minutes with a clinical finish, and played his part in setting up Willian for Chelsea's second a few minutes later.
Brighton were denied an opportunity to get back into the game when referee Jonathan Moss turned down two first-half penalty appeals for fouls on Ezequiel Schelotto.
The Seagulls could not contain Hazard and he doubled his own tally on 77 minutes, before Victor Moses rounded off the scoring one minute from time.
Relive how the action unfolded with our minute-by-minute updates from the South Coast below.
11.30amIt is another miserable January day on the South Coast, but there is a full day of Premier League action to perk us up, starting with Chelsea's trip to the Amex Stadium to face Brighton & Hove Albion. Both sides are in need of the points for very different reasons, so let's get to the team news...
11.36amWith Morata and Pedro suspended following their red cards against Norwich in midweek, Michy Batshuayi is given a rare chance to lead the line. It could be the Belgian's last chance to save his Chelsea career, with the Blues linked with a host of forwards this week.
11.38amAn ankle injury keeps Thibaut Courtois out so this season's cup hero Willy Caballero makes his Premier League debut for Chelsea in goal - he made 21 in three seasons at Manchester City.
11.40amThat is one of four changes from Chelsea's last Premier League outing - the 0-0 home draw with Leicester City. Injuries have hit them hard with Gary Cahill and Cesc Fabregas missing with hamstring strains, and Danny Drinkwater also absent, so there are recalls for Andres Christensen and Willian.
11.42amNew signing Ross Barkley makes the Chelsea bench for the first time after his £15m arrival from Everton. The England midfielder played 70 minutes in a behind-closed-doors game in midweek after recovering from a ruptured hamstring which has kept him from playing at all this season.
11.44amAside from Barkley, the visiting bench looks very thin with this stretched Chelsea squad exposed for a lack of depth in forward areas. Charly Musonda is the only other attacking option and is joined among the substitutes by fellow youngsters Ethan Ampadu and Dujon Sterling.
11.46pmPerhaps that is why Antonio Conte has been searching frantically for a striker in this transfer window. Andy Carroll and Peter Crouch are a couple of the surprise names that have been reported as options for Chelsea, who have hit a drought with Morata's six-game barren spell.
11.48amSpeaking of new strikers, Brighton broke their transfer record last night to sign Jurgen Locadia from PSV Eindhoven for £14m. The 24-year-old Dutchman has scored nine goals in 15 matches Eredevisie matches this season, but was not registered in time to be available to Chris Hughton today.
11.50amHughton appears to have opted for a change in system today, with Connor Goldson being drafted in to make a back three alongside Lewis Dunk and Shane Duffy. The former Shrewsbury defender had been touted for a loan move earlier this week, but now faces the challenge of Eden Hazard et al.
11.52amThere are five Brighton changes in total from the 2-0 defeat to West Bromwich Albion, including two at full-back as Bruno and Gaetan Bong drop out and Ezequiel Schelotto and Markus Suttner come in, probably as a result of Hughton wanting more going forward with the switch to wing-backs.
11.54amSolly March completes the three-man midfield alongside Dale Stephens and Davy Propper, who have each started every Premier League game of the campaign. Chief creator Pascal Gross, who has only one goal or assist in his last 11 league matches, will play just ahead of them.
11.56amUp front, Tommer Hemed makes his first start since Brighton lost the reverse fixture 2-0 on Boxing Day. Glenn Murray is demoted to the bench alongside Jose Izquierdo, who give the Seagulls goalscoring options to turn to late on if they can stay in the game. No Anthony Knockaert in the squad though.
11.58amSTAT: Brighton are the only team in the Premier League yet to take a point off any of the top-six teams this season. They have only scored one goal in those six matches too - a consolation in a 5-1 thrashing by Liverpool. Perhaps that explains Hughton's tactical switch today.
12.00pmThe extra centre-back may also be designed to combat Brighton's problems defending dead-ball situations. The Seagulls have conceded a league-high 16 goals from set-pieces in 2017-18, which is over half the goals that they have conceded. That really is a staggeringly poor record.
12.02pmWhen you match that record with Brighton's 17 goals from 23 league matches this season, which makes them the second lowest scorers in the division behind Swansea City, it is easy to see how they have been sucked into relegation trouble. Albion are down to 16th, only three points above water.
12.04pmBrighton's next league goal will be their 200th in the top flight, which would be a nice feather in the cap for someone like Hemed or March this afternoon, or maybe Murray off the bench. There of course was a 34-year gap in their top-flight history before Hughton led them to promotion last season.
12.06pmAlbion have never beaten the reigning top-flight champions in a league match, losing seven and drawing two of their nine fixtures. With Chelsea's injury and suspension problems, today seems like a good chance for them to end that run although Hughton's team selection is designed to contain.
12.08pmThe key to Brighton's fate this season is likely to be their home form. The Seagulls have lost only two of their 11 Premier League fixtures at the Amex this term, although they may need to convert some draws into wins with the spoils having been shared in six of those encounters.
12.10pmOnto Chelsea, who could remain winless in their opening three Premier League matches of a calendar year for the first time in 23 years. The Blues have drawn all five of their games in 2018 - inside 90 minutes - but did progress to the fourth round of the FA Cup on penalties against Norwich City.
12.12pmThe out-of-form Blues could also go three league away games without a win for the first time under Conte. Their only victory in their last six away games in league and cup was the 3-1 win at Huddersfield Town in December.
12.14pmAll eyes will be on Batshuayi today, who makes only his fifth start from 33 Premier League appearances. The Belgian has done a good job for Chelsea as an impact substitutes, with seven goals off the bench since the start of last season, but he clearly does not have the full trust of his manager.
This is an opportunity for him to change all that, and if he doesn't then he might be moved out of Stamford Bridge before January 31.
12.16pmMorata has come in for plenty of criticism of late, having missed some golden chances particularly in two games against Arsenal, but Hazard must also shoulder some blame for Chelsea's run of one goal in four. The PFA Player of the Year holder has one goal or assist in his last nine league outings.
12.18pmSTAT: The Blues have lost just one of their 27 Premier League matches as reigning champions versus promoted opposition - 21 wins and five draws. That was a 1-0 home defeat by Bournemouth in 2015, and a good omen for Brighton is that the winner was scored by their own Glenn Murray.
12.20pmHEAD TO HEAD: Brighton have lost their last seven games against Chelsea in all competitions, failing to score in six of them. Their only ever win against the Londoners came in the first meeting in 1933 - a 2-1 home victory in the FA Cup, long before the Amex Stadium was built.
12.22pmLocadia has just been introduced to the Brighton fans, receiving a very warm ovation. In an interview with Sky Sports, the Dutchman has revealed that he is carrying an injury, so it might be a few weeks before he is able to have an impact on their battle to retain their Premier League status.
12.24pmJust over five minutes until kickoff on a wet and misty South Coast, where Jonathan Moss is our referee.
12.26pmThis is the 150th league game at the Amex Stadium, and Brighton would love to mark it with a win which would see them climb to 11th in the table. Chelsea need the points too, though, in their battle for the top four now that only three points separate them and fifth-place Tottenham Hotspur.
12.28pmPREDICTION: This depleted Chelsea team could be there for the taking this afternoon. I'm not sure that Brighton have the firepower to win the game but I do fancy them to hold the Blues to a 1-1 draw.
1 minKICKOFF: Chelsea get the game underway, with both sides wearing black armbands in tribute to former West Brom and Coventry player Cyril Regis, who passed away this week.
2 minHazard wins Chelsea an early free kick - the Belgian may not have been at his best lately but is still the most fouled player in the division. Willian curls the set piece straight into the arms of Matt Ryan.
3 minIt is a lightening-quick start for Chelsea as Hazard clinically fires them into a third-minute lead. Moses's cross takes a deflection off Stephens and falls at the feet of the Belgian, who has too much space in the box and takes full advantage with an emphatic touch and right-footed finish from 12 yards.
5 minDecent response from Brighton as March gets forward down the right and whips the ball across. It is cleared as far as Gross, who drills a shot over the crossbar from 25 yards.
6 minThis is fast turning into a nightmare for Brighton, but it really is a dreamy goal for Chelsea. Hazard, Batshuayi and Willian combine with a series of one-touch passes and flicks on the edge of the box, and the latter unleashes a powerful 20-yard drive which is past Ryan before he can see it.
10 minThis is now an incredibly difficult task for Brighton as the onus is on them to break down Chelsea, which is not their strength. The visitors meanwhile can afford to invite the Seagulls onto them and hit them on the break through Hazard and Willian. So, in summary, Brighton might be screwed already.
12 minSchelotto finds some space over on the right byline but badly overhits his cross with only Hemed in the box.
14 minSHOT! Rudiger gives the ball away with a sloppy pass out from the back. Propper feeds the ball into March, whose silky footwork shakes off Kante - an almost impossible task - but the subsequent shot is weak and easy for Caballero.
16 minPENALTY APPEAL! Chaos in the Chelsea box as Cabellero flies off his line to punch clear a long ball destined for Gross. The goalkeeper jumps back to his feet to win the second ball, btu Scheletto beats him to it and the Argentine takes him down. It is a stonewall penalty which is not given by Jonathan Moss, whose line of sight may have been blocked by Bakayoko.
What would VAR have made of that?
18 minSHOT! The visitors look really potent on every attack, with Hazard at the centre of everything. Brighton have enough bodies back to cope with the threat, but Chelsea are passing the ball so quickly and another slick move ends with Bakayoko drilling a low shot why Ryan pushes away.
20 minCaballero is getting away with murder here. He flaps at a Brighton corner and is saved by the offside flag as Propper tries to flick the ball backwards into the vacant net after Duffy won the second ball. The improvised header rolls just wide, but Caballero is giving Brighton to some to cling onto.
22 minGood play from Batshuayi, who holds off Dunk and nearly slips a pass into the path of Hazard only for Duffy to stick a foot out to make the interception.
24 minGross floats a free kick towards the penalty spot where strong defending from Rudiger prevents Duffy from getting his head on the end of it. The follow-up drops to Suttner who drags a shot wide.
26 minSHOT! Chelsea spring on Brighton and Willian has a free run behind Dunk in the right channel. Hazard finds the Brazilian, whose powerful strike is pushed behind for a corner by Ryan at his near post.
28 minSAVE! Hazard has this Brighton defence at his mercy today. He passes up a couple of his own opportunities to shoot to set up Batshuayi, who cuts inside onto his left foot and forces another strong stop from Ryan.
30 minSAVE! We've seen the worse of Caballero and now we see the best - a wonderful one-handed reaction save to keep out Hemed's close-range header. Brighton had two men unmarked at the back post from Gross's cross, but their stand-in keeper came to their rescue.
32 minCHANCE! Scheletto gets the Amex on their feet with some admirable high pressing, and two crunching tackles which earns Brighton a corner, from which another chance goes begging as Duffy glances a header wide. The defender barely got any contact on another superb delivery from Gross.
34 minA couple of times now, Brighton have got in behind the Chelsea defence with raking long balls to March and Gross, which is a reason for them to stay encouraged. Another one is the unpredictability of Caballero, whose wild punch from Suttner's cross could have gone anywhere.
36 minYELLOW: Scheletto has a second penalty shout when he goes down under the challenge of Bakayoko. The Italy international has less of a case this time, although there was a tangle of legs and the Brighton player's frustration costs him a yellow card for dissent.
38 minChelsea may have been unhappy with the impact of VAR in midweek, but all of the decisions have gone their way so far this afternoon, and that would not have been the case if technology was in play.
40 minSchelotto has been a good outlet for Brighton and it is clear to see why he got the nod over adored skipper Bruno, the oldest player in the Premier League this season at 37, in this changed system.
41 minIt takes Chelsea only two touches to open up the Brighton defence with an excellent first-time pick out by Kante to Hazard, who swiftly loses his marker only for his second touch, a cross-cum-shot with his left foot, to be out of the reach of the diving Moses at the back post.
43 minBatshuayi will be desperate to get on the scoresheet, but this shot on the turn from 22 yards, with his weaker left foot, was a touch ambitious and flies harmlessly wide of Ryan's net.
45 minFor the upteenth time this half, Hazard and Willian combine to test the Brighton defence. Suttner stands up well at first by tackling Willian, but then trips Hazard right on the edge of the box. Referee Moss again waves play on, and this one would have been a free kick rather than a penalty anyway.
1.22pmThe half-time scoreline at the Amex only tells half the story. Yes, Chelsea raced into a 2-0 lead with some sumptuous early attacking play, but Brighton have hit back and have been unlucky not to have at least one penalty, nor pull one back when Caballero saved brilliantly from Hemed's header.
1.24pmHazard has been nothing short of magical in the opening 45 minutes. The Belgian got his goal on three minutes - an emphatic touch and finish inside the box - and then more than played his part in Willian's strike only three minutes later. Brighton have not been able to get anywhere near him.
1.26pmNo goal so far for Batshuayi, but any watching managers will have seen plenty to work with, even if Antonio Conte does not. The Belgian has occupied Brighton's back three to create space for Hazard and Willian and has been involved in some delightful build-up play.
1.28pmChris Hughton was chatting referee Jon Moss's ear off as they left the field for half time. Brighton had two penalty appeals, and should feel particularly aggreived by the first one when Caballero blatantly tripped Schelotto. The problem was, Moss's view was blocked by Bakayoko.
1.30pmThe Seagulls have looked slightly more vulnerable from open play than usual, but that is down to the brilliance of Hazard and company. Going forward, Brighton have caused Chelsea issues especially when they have gone more direct. An early goal in the second half would give them great encouragement.
1.32pmSolly March is thriving in his free role behind the striker, but if Hughton wanted to revert to the usual four-at-the-back system, he could bring on Jose Izquierdo in the second half and really try to stretch Chelsea in behind the wing-backs, where the visitors have appeared a little vulnerable.
46 minKICKOFF: Brighton get us back underway with both sides unchanged and the hosts sticking with the same system.
48 minThere is a stoppage in play following a clash of heads between Duffy and Christiansen, who did brilliantly to divert Suttner's set-piece delivery away from the Brighton defender but took a nasty blow for his troubles. The Dane looks a little dazed but has been given the thumbs up by Chelsea's physio.
50 minWOODWORK! Lady luck continues to work against Brighton as Propper thumps a header against the post. The move started with Schelotto again down the right, and he laid the ball off for Gross whose cross was powered past Caballero but rebounded off the woodwork.
52 minIt would have been easy for Brighton's heads to drop after conceding those two early goals, but they have kept themselves in the game and continue to ask questions of the Chelsea defence.
54 minThe change of formation may have caused some early defensive uncertainty for Brighton, but it also seems to have made them more of an attacking threat and I wonder if it is something he will persist with against lesser opposition.
56 minYELLOW: Hazard gets floored by a hard but clean Stephens slide tackle, but gets back up again to continue running at the Brighton defence and is eventually felled by Shane Duffy, who goes into the book.
58 minSAVE! From the resultant free kick, Willian brings out a wonderful save from Ryan, who tips the Brazilian's over-the-wall curler onto the post. Meanwhile, David Luiz is on for Christiansen who was ushered off by Jon Moss after failing to recover from his knock to the dead.
60 minLuiz has slipped straight into the middle of the Chelsea back three. If that is a concussion for Christiansen then the Brazilian is likely to be required for the EFL Cup semi-final second leg with Arsenal on Wednesday.
62 minMarch collects a pass inside from Schelotto and has a go on goal, with Caballero pushing the ball around the post. He could have returned the ball out wide but the midfielder is playing with confidence this afternoon and took the shot on himself.
64 minGlenn Murray and Ross Barkley are both going through extensive warm-ups on the sidelines...
66 minSAVE! Schelotto's energy has been incredible this afternoon. He pinches the ball from Alonso on the edge of the box and runs in on goal, but Caballero is off his line to make a crucial block from the wing-back's poked finish.
68 minSUBSTITUTIONS: Double change for Brighton as Murray and Beram Kayal are on for Gross and Hemed, who can both be proud of decent performances which were simply without luck.
70 minAnother blank today would mean that Brighton have failed to score in nine of their last 12 league games. That would not be a fair reflection of the problems that they have caused Chelsea this afternoon though. They deserve a goal even if it ends up only being a consolation.
73 minMarch makes a run to the back post but Murray can't pick him out with a drilled cross which Caballero intercepts.
75 minSUBSTITUTION: Chelsea make their second change, but it isn't Barkley yet. Zappacosta comes on to replace Alonso, who has not had his usual influence on this game from either a defensive or attacking perspective.
77 minBrighton's brave effort will count for nothing because Hazard has wrapped this game up for Chelsea with a deserved second. Goldson backs off and backs off as the Belgian runs at the Brighton defence, and he takes up the shooting invitation to calmly slot into the bottom corner from 18 yards.
79 minThat is eight league goals for the season for Hazard, 11 in all competitions. Willian, with a perfectly-weighted pass, picked up the assist for any Fantasy Football managers keeping count.
81 minSUBSTITUTION: There will be no Ross Barkley debut today. Charly Musonda is Chelsea's final substitute, coming on for Willian who has been excellent and yet a distant second to Hazard.
83 minSUBSTITUTION: Hughton responds with his final change as Izquierdo replaces March, who has been very lively in a new role today. An experiment worth persisting with for Brighton.
85 minHazard embarks on another mazy dribble across the box before shifting the ball on for Batshuayi, whose left-footed shot lacked any sort of conviction and rolls into the arms of Ryan.
88 minChelsea are in cruise mode now but it hasn't always been that way. They have been made to work hard by Brighton and these match could have had a very different complexion had Brighton got one of those first-half penalty appeals.
89 minVictor Moses pours salt into the Brighton wounds with a Chelsea fourth, making an out-to-in run which Musonda finds with a beautiful lofted pass. The control from Moses is just as good and he stabs the ball around Ryan for his first league goal in 14 months.
90+1 minThere will be THREE minutes of stoppage time. Kayal crosses towards Murray who gets above Luiz but can't control his header which rises over the crossbar.
90+2 minAzpilicueta throws himself in front of a shot from Izquierdo to make a block which preserves Chelsea's clean sheet.
2.28pmA first win of 2018 for Chelsea which looks emphatic by full time but was not always easy against a Brighton side who showed great spirit to respond to their nightmare start, and should have had at least one penalty in the first half. There is no stopping Hazard in that mood though.