Kenedy and Charly Musonda were on the scoresheet either side of the Belgian's opening goal as the Blues steamrollered Forest in the first half.
Making his first start of the season following ankle surgery, Eden Hazard unselfishly supplied Batshuayi with his second four minutes after the break.
His treble was completed in fortuitous fashion on 84 minutes as Kenedy's shot rebounded off the crossbar and back into the net off Batshuayi, but there was still time for Tendai Darikwa to grab the visitors a stoppage-time consolation.
Relive how the action unfolded at Stamford Bridge with Sports Mole's minute-by-minute updates.
6.45pmEvening all! Chelsea begin their Carabao Cup campaign with the visit of Nottingham Forest tonight. We already know Eden Hazard will be starting this evening, but what about the rest of the team news?
6.51pmNine changes in total from Conte, with Cahill and Fabregas the only players retained from Sunday's 0-0 draw with Arsenal. Hazard's first start this season comes alongside Michy Batshuayi and Charly Musonda in the front three.
6.53pmWilly Caballero makes his Chelsea debut in goal following his free transfer from Manchester City. Antonio Rudiger and Andreas Christiansen come into the back three with David Luiz unavailable through suspension.
6.55pmSummer signing Davide Zappacosta starts at right wing-back. He made quite an impact on his debut - a freak goal from 25 yards out against Qarabag in the Champions League. There are also starts for Tiemoue Bakayoko and Kenedy, who was sent home from Chelsea's tour of China because of offensive social media posts, across the midfield.
6.57pmAntonio Conte has Alvaro Morata and Willian in reserve on the bench, alongside a bunch of youngsters including Jake Clarke-Salter and 17-year-old Ethan Ampadu. The likes of Cesar Azpilicueta, Ngolo Kante, Thibaut Courtois, Pedro and Marcos Alonso have the night off.
6.59pmThere are wholesale changes for Forest, also. Mark Warburton makes eight alterations from Saturday's 2-1 defeat to Wolves, including recalling second-round hero Tyler Walker up front alongside Jason Cummings.
7.01pmFormer Chelsea prospect Michael Mancienne is back to captains the Tricky Trees as they match up the Blues with a 3-5-2 formation. Jack Hobbs also starts in defence as Armand Traore and Matt Mills drop out.
7.03pmLocal boy done good Joe Worrall and midfielders Ben Osborn and Kieran Dowell, on loan from Everton, are the Forest players who pull double duty. Stephen Henderson replaces Jordan Smith in goal and there are also opportunities for Eric Lichaj, Danny Fox and Andreas Bouchalakis.
7.05pmThe visitors have not brought top scorer Daryl Murphy with them to London, but have plenty of attacking options on the bench. Teenage hotshot Ben Brereton could be turned to later in the action.
7.07pmChelsea have not lost a home League Cup tie since the semi finals of the 2012-13 season when they went down 2-0 to Swansea. Although it is the reverse leg at the Liberty Stadium that is more widely remembered, for Hazard kicking a ballboy.
7.09pmJose Mourinho won the League Cup three times at Chelsea - in 2005, 2007 and 2015. Their other triumphs came in 1998 (Gianluca Vialli) and 1965 (Tommy Docherty). Formula: Win League Cup: become a Chelsea legend.
7.11pmOf the matchday 18 from Chelsea's victory over Tottenham at Wembley (obviously) two years ago, only six remain at Stamford Bridge. Of those six, Hazard Cahill and Fabregas all start this evening.
7.13pmCaballero also owns a League Cup winners's medal. He was Manchester City's hero in the 2016 League Cup final, when he saved penalties from Lucas Leiva, Philippe Coutinho and Adam Lallana in a shootout win over Liverpool.
7.15pmChelsea will be looking to relocate their shooting boots tonight. Sunday's 0-0 stalemate with Arsenal was the first time that they had failed to find the back of the net in 15 attempts, and it was their first scoreless draw in 73 matches.
7.17pmDavid Luiz's red card against the Gunners was already Chelsea's third of the season. At this rate they are in danger of eclipsing Arsenal's unwanted record of 12 in a Premier League season.
7.19pmChelsea's 10 points from their opening five league games is the same return that they have managed in three of the previous five seasons, including in 2016-17 when they went on to lift the title.
7.21pmForest have lifted this trophy on four occasions, most recently in 1990. That triumph made them the joint-most successful team in League Cup history, although they have since been overtaken by Aston Villa, Manchester United, Liverpool and tonight's opponents.
7.23pmHowever, their recent performances in the competition have been dire. The Midlanders have not made it past the third round of the League Cup since 2004. Mark Warburton is manager number 18 since that date.
7.25pmJason Cummings is the joint-second top goalscorer in the League Cup this season. Forest's summer signing from Hibs has three goals in the competition thus far - only Leeds forward Samuel Saiz has more. The Scottish striker has only started one Championship game though, so has a point to prove.
7.27pmWith Cummings, Murphy, Walker, Brereton, Murphy and Vellios to call upon, the Tricky Trees carry a goal threat on the road. They have scored in all four of their Championship away games this season and notched three times at St James' Park in the last round.
7.29pmThere is an air of positivity around the City Ground these days with Warburton in charge. However, they are only one point better off than they were at this stage last season under Philippe Montanier. He was sacked in January. You never can tell in football, these days.
7.31pmForest have slipped to 10th in the Championship table, having lost three of their last four matches in the Championship, although two of those defeats have come against early pacesetters Leeds and Wolves. It is not the huge gap in the football league pyramid that romanticises cup ties, but it is big enough to make them huge underdogs.
7.33pmThey may be in the top half, but their 13 goals conceded in eight games is the fourth worst defensive record in the Championship. They have been scored past more than Brentford, who are yet to win a game.
7.35pmTen minutes until kickoff at Stamford Bridge. A victory for Forest this evening would be a fitting tribute to their double European Cup-winning manager Brian Clough, who passed away 13 years ago today.
7.37pmHEAD-TO-HEAD Clough was in charge of Forest for their biggest victory over Chelsea; a 7-0 thrashing at the City Ground in 1991. They also beat the Blues 6-0 when they were English champions in the late 1970s.
7.39pmHowever, Forest have never beaten Chelsea in this competition, and have lost their last four meetings with the Londoners. Andriy Shevchenko and Didier Drogba were scorers as Chelsea ran away with their last encounter 3-0 - a third-round FA Cup clash in 2007.
7.41pmAs might be expected, the Blues have a dominant record against their visitors at Stamford Bridge. Forest have won on only one of their last 11 visits to Chelsea's turf - that was back in 1995.
7.43pmPREDICTION: Home advantage should make this a comfortable night for Chelsea. If it was at the City Ground, Forest might give this much-changed lineup a game. As it is, I expect a 3-0 win.
1 minThe action is underway at the Bridge, with both teams in their traditional kits...
3 minThe visiting Forest supporters are in good voice in the early stages. Around 4,000 of them have travelled from the Midlands in the hope of their team claiming a famous scalp.
5 minCaballero has some early work to do as Bouchalakis strikes from range after good work down the Forest left. The Greek scored a couple of stunners from distance at Brentford last month.
6 minDowell fails to make the most of an advantage given to Everton and is eventually crowded out by Cahill and Kenedy on the right edge of the box. That was a promising situation wasted by Forest.
8 minWorrall makes a crucial tackle to deny Musonda after some dallying on the ball at the back had allowed Bakayoko to thread the youngster through. It is a first senior start for the Chelsea youngster.
11 minBatshuayi gets away from Hobbs in the box with a nice first touch, only to drag his left-footed shot a few yards wide of the post. I wonder if the FIFA boffins are watching after his Twitter bantz with EA Sport?
13 minEarly breakthrough for Chelsea and it comes through their Twitter reprobate! Rudiger strolls out from the back unchallenged and knocks an inviting ball to the far post, which Kenedy meets sweetly on the volley. Very tidy finish which left Henderson with no little chance.
15 minThat is Kenedy's first Chelsea goal since scoring against Walsall in the same round of the same competition two years ago. He had a forgetful year on loan at Watford last season, so will have enjoyed that.
18 minChelsea are well on their way already as Batshuayi makes it two inside 20 minutes. The Belgian runs onto Hazard's deflected through pass and pokes it through the legs of Henderson for his second of the season.
21 minYELLOW! Hobbs earns himself a booking for dragging back Bakayoko. Warburton will be disappointed with his side's defending for both goals and they continue to be at sixes and sevens.
23 minFabregas and Hazard take turns to release Kenedy down the left with sublime passes. From the Belgian's back-heel, the Brazilian charges to the byline and fizzes in a wonderful cross which is just in front of Musonda and Batshuayi.
24 minThe Spaniard digs into his bag of passes once more to lift a ball over the top for Zappacosta, who controls nicely and slots the ball home on his left foot, but the wing-back was comfortably offside.
27 minWOODWORK! Forest nearly pull one back from a superb Dowell free kick which strikes the crossbar. Caballero was completely beaten but the shot did not quite have the dip. Very unlucky.
29 minThat effort from Dowell goes to show that Forest have quality in the final third, even without a couple of their first-choice attackers. It is at the other end where they have major problems.
30 minTyler Walker was in Des Walker territory there and got himself into a right mess. In his own box, the son of the former England defender is dispossessed by Bakayoko, but the resulting shot from Musonda is blocked.
32 minKenedy has Henderson worried with a 25-yard rocket which swerves a few yards wide of his post. The Brazilian is looking for his second goal, although I'm sure all of the Chelsea team will be looking to get in on the act now that they have seen the vulnerability of this Forest defence.
35 minSpeaking of people who have two goals, Marcus Rashford is already at the double tonight for Manchester United in their tie with Burton Albion, continuing his excellent early-season form. Arsenal and Manchester City also lead against Doncaster and West Brom, so it is looking good for the big boys.
37 minBakayoko stings the gloves of Henderson with a 30-yard piledriver that was straight at the Irish goalkeeper. He certainly got some power on that; had it been in a corner they'd have been no stopping it.
40 minA wonderful moment for full debutant Musonda, who wheels away screaming as though he has scored in the World Cup final to mark his first Chelsea goal! And he adds a dive for good measure! Fabregas opens up the Forest defence with a lovely little reverse pass and Musonda thumps it low and hard through Henderson, who should do better.
42 minChelsea have not even got out of second gear and they are 3-0 up. This could be anything by full time. Forest will wonder how it has got this bad, this quickly, when they have had some nice passages on the ball, but they have just been far too easy to break down.
44 minForest's humbling half is summed up by goalkeeper Henderson slipping as he attempts a clearance and conceding a corner. They would have hoped to put in a much better showing than this.
45 min+2CHANCE! Musonda goes so close to a second, and he would have owed it to Fabregas, whose outstanding 50-yard pass picked out the run of the 20-year-old. His control was also very good, and he beat the onrushing Henderson to the ball, but his prod rolled just wide of the post.
8.36pmThis has been an absolute walk in the park for the hosts. Hazard started, but it is youngsters Kenedy and Musonda who have got on the scoresheet either side of a strike from Batshuayi.
8.39pmFabregas has completely ran the game from midfield. His range of passing has been a joy to behold, although he has been presented with some large gaps to aim for by the Forest defence.
8.41pmMark Warburton will be bitterly disappointed with how easily his team have bowed down to the champions. Goalkeeper Henderson was arguably culpable for the third goal, and the opening two were simply cases of not tracking runners. Very sloppy defending.
8.44pmSTATS: Little surprise to see that Chelsea have dominated possession with 66%, or that they have had six shots on target compared to Forest's one. Hobbs is the only man booked for either side.
8.46pmForest's best moment of the half was a Kieran Dowell free kick which struck the crossbar. The visitors started brightly on the ball, but have had the confidence knocked out of them by the events at the other end.
46 minForest resume the action, with both sides unchanged. They will be hoping to keep it respectable in the second half and possibly pinch a goal. Chelsea will have a five or six goal win in their sights.
47 minSHOT! The Tricky Trees start the half brightly again and engineer an opening for Osborn, whose shot is unconvincingly parried away by Caballero, and Chelsea clear the loose ball.
48 minWOODWORK! Hazard nearly gets himself a goal with a piece of individual brilliance. He leaves Mancienne on the floor, glides away from Worrall and whips his foot around a shot which cannons back off the post. Henderson was nowhere near it; saved by his post.
51 minWe saw glimpses of Hazard's magic in the first period, and he has started this half very confidently. I wonder if Conte will pull him after 70 minutes or try to get 90 minutes in the Belgian's legs.
53 minBatshuayi has his second, but this is all about Hazard. World-class play from the winger, who latches onto a Fabregas pass and stays on his feet under the challenge of Worrall. He rounds Henderson, only to then turn his back on a vacant goal and square to Batshuayi to slot home for a simple finish. Brilliant.
56 minSUBSTITUTION: And with that fourth goal, Conte makes his first change. Seventeen-year-old midfielder Ethan Ampadu is on for his Chelsea debut in place of Fabregas, who has been masterful.
57 minA smartly-worked corner tees up Dowell for a shot which whistles past Caballero's post. The Blues keeper may have had that covered, but the Everton loanee showed great technique with that first-time hit on his left foot.
59 minSUBSTITUTION: Ampadu's first involvement is to, fairly, crunch Danny Fox. The experienced wing-back was about to be replaced by Tendai Darikwa anyway, so Warburton uses the stoppage to make his change.
62 minA deflected cross from Darikwa briefly threatens the Chelsea goal before landing on the roof of the net. The signing from Burnley has gone to the right flank, with Lichaj switched to the left.
65 minZappacosta, who hasn't seen as much of the ball as Kenedy on the opposite wing, gets to the right byline but sees his cross towards the six-yard box cleared at the near post by Hobbs.
66 minSUBSTITUTION: Warburton swaps one young striker for another as Brereton replaces Ward. The 18-year-old, who spent time at the Manchester United and Stoke City academies, is very highly rated by fans of the Midlands outfit.
69 minBrereton runs onto a ball over the top but does not quite have the pace to get away from Zappacosta, whose pressure forces the teenage forward to slice his left-footed shot harmlessly off target.
71 minSUBSTITUTION: Conte makes his second sub, giving an opportunity to 19-year-old Jake Clarke-Salter in place of the largely untested Christiansen. Who says Chelsea don't give kids a chance?!
73 minIt is tricks and flicks time for Chelsea now. Kenedy tries something fancy in the box when there were four or five bodies waiting for a cross. Not sure that will help him get back in Conte's good books.
76 minSUBSTITUTION: Each manager makes their final change. Dujon Sterling is another 17-year-old debutant for Chelsea as Zappacosta comes off. Dowell has been Forest's best player tonight and is spared 20 more minutes of torture as Zach Clough comes on for a run out.
78 minThose changes mean that Hazard will complete 90 minutes. Conte will be very pleased with what he's seen from the Belgian, but his non-withdrawal is a sign that he probably won't start this weekend.
81 minCLOSE! Good work from Brereton earns Forest a free kick in the left channel. Clough tries a sneaky shot from a tight angle and the scrambling Caballero would have been in trouble had the ball dropped only a yard or two more.
84 minIt is easy to play when your team is 4-0 up, but Ampadu does look very comfortable on the ball. He's also built very physically, as Danny Fox found out earlier. One to watch out for, certainly!
85 minChelsea make it five and Batshuayi has the match ball, not that he knew anything about his hat-trick goal. Kenedy smashes a shot from the left edge of the box against the crossbar, and the rebound hits the Belgian on its way back into an unguarded net. They all count!
87 minA low skimmer from Cummings gives Cabellero some late work to do. Conte will be eager to ensure that this excellent night's work is not marred by a late goal conceded. Italians love clean sheets!
90 minJust one more minute for Forest to endure as we enter stoppage time...
90+1 minBut they don't endure it, they enjoy it as Darikwa grabs them a consolation with the last kick of the game. Forest countered nicely through Darikwa and Osborn, and the ball eventually fell to the substitute for him to finish past Caballero from eight yards.
9.39pmForest fans have something to talk about on the way back to Nottingham tonight, but they were throughly outclassed tonight. Batshuayi will take the headlines for his hat-trick, but Fabregas and Hazard were outstanding, and young goalscorer Charly Musonda deserves a mention too.
9.42pmThanks for joining us this evening to follow Chelsea's easy passage into the Carabao Cup fourth round. Learn who they will face next with Sports Mole this evening as we will have all the reaction to the draw. Until next time!