It took just three minutes for the Belgian to open the scoring as he ran onto a through-ball from Juan Mata and cut back onto his right foot before slotting past Jonas Lossl.
Juan Mata thought that he had doubled United's lead in first-half stoppage time but his effort was controversially ruled out for offside after Kevin Friend referred to VAR.
The Red Devils were two goals up 10 minutes into the second half as Lukaku finished clinically again, having been released by a defence-splitting pass from Alexis Sanchez.
Relive how the action unfolded at the John Smith's Stadium with our minute-by-minute updates below.
4.30pmHuddersfield sent shockwaves through the Premier League when they beat Manchester United at the John Smith's Stadium in October, and the Red Devils got some retribution at Old Trafford a fortnight ago. Who will win this rubber match and advance to the quarter-finals of the FA Cup?
4.36pmAs was announced earlier today, Paul Pogba misses out through illness, on the week that Jose Mourinho was forced to rubbish speculation that the midfielder wants to leave Old Trafford. You can make your own minds up on that one.
4.38pmWith Ander Herrera also missing with a muscle injury, there is just a third start of the season for the veteran Michael Carrick, and Mourinho partners old with young as Scott McTominay completes the midfield three alongside Nemanja Matic.
4.40pmUnited fans may have been hoping to see Eric Bailly today as the defender recovers from ankle surgery which has sidelined him for three months. The Ivorian is only on the bench but there is a recall for Victor Lindelof at centre-back. His only starts since New Year's Day have been in the FA Cup.
4.42pmAfter losing his place in the Premier League team to the fit-again Ashley Young, 'best left-back in the world', or 'overweight lazy youngster' depending on Jose Mourinho's mood, Luke Shaw is restored to the starting lineup. Young also starts on the right as Antonio Valencia is afforded a rest.
4.44pmDavid de Gea and Phil Jones are also given the afternoon off, while Jesse Lingard and Anthony Martial drop to the bench. Juan Mata and Alexis Sanchez start either side of Romelu Lukaku in a front three that Mourinho will hope can fire them through to the last eight at the John Smith's Stadium.
4.46pmHuddersfield boss David Wagner makes four changes to the side which thrashed Bournemouth 4-1 in their last outing. Talisman Aaron Mooy is out with a knee injury and Jonathan Hogg also drops to the bench as Danny Williams and Philip Billing come into a new-look four-man midfield.
4.48pmSteve Mounie has rediscovered his promising early-season form after recovering from injury, with three goals in five matches, and today is partnered by Collin Quaner in attack. The German is still waiting for his first goal of the season, having made 22 appearances in all competitions.
4.50pmAlex Pritchard is ineligible having featured for Norwich City already in the FA Cup this season, and January signing from Monaco Terence Kongolo is given a chance at left-back ahead of Scott Malone.
4.52pmAcademy youngsters Ethan Hamilton and Angel Gomes make the United bench as Mourinho has to make do without Marouane Fellaini, Daley Blind and Marcus Rashford as well as Pogba et al.
4.54pmSTAT: Huddersfield are appearing in the fifth round of the FA Cup for only the fourth time since 1998. The last time that they reached the quarter-final was back in 1972.
4.56pmUnited, winners of the FA Cup only two season's ago, have progressed past the fifth round the past eight times they have reached this stage. The previous two clubs to have knocked them out of the last 16 have gone on to win the trophy (Liverpool in 2006 and Arsenal in 2003).
4.58pmJust a reminder that VAR will be in use today, should referee Kevin Friend require its assistance. It has caused controversy in the previous rounds, but not yet this weekend. There is still time, though, and controversy seems to follow Jose Mourinho wherever he goes...
5.00pmThe Special One has been, typically, the centre of attention in the build up to this match, describing reports of Paul Pogba's unhappiness at United as "lies", although he did not protect the £85m Frenchman from criticism over his recent performances saying "he has not been playing well."
5.02pmIf there is any secret unrest behind the scenes, Pogba is towing the party line...
Gutted I won't be at Huddersfield but I need to get better. Come on United 👊🏾 @ManUtd
5.04pmRESULTS: Southampton and Brighton & Hove Albion have joined Leicester City and Chelsea in the hat for the quarter-final draw with victories over West Bromwich Albion and Coventry City respectively. Sheffield Wednesday and Swansea City will go to a replay after a 0-0 draw in Yorkshire.
5.06pmSTAT: Huddersfield have won their past two games by a 4-1 scoreline, although they needed extra time to eventually beat Birmingham in their FA Cup fourth-round replay. They last scored four or more goals in three consecutive matches in January 1928, and you'd get long odds on that today.
5.08pmIn between beating Huddersfield 2-0 at Old Trafford a fortnight ago, United have lost consecutive away matches to Tottenham Hotspur and Newcastle United. A third defeat in a row on their travels would be the first time that has happened since December 2015 when Louis van Gaal was manager.
5.10pmAlexis Sanchez opened his Red Devils account against the Terriers, and few would bet on him getting on the scoresheet again today considering his FA Cup record. He has been directly involved in 15 goals in 15 appearances - eight goals and seven assists - including strikes in the 2015 and 2017 finals.
5.12pmThe Red Devils have another cup expert in their ranks in Jesse Lingard. The attacking midfielder has scored in all four of United's domestic cup matches this season, and in the 2016 final against Crystal Palace. A good player for Mourinho to have in reserve if needed, then.
5.14pmOne player that Mourinho won't be able to call on this afternoon is Marcus Rashford. The England forward, having only started two matches in 2018, would have been hoping for a chance to prove himself in the first team but a muscle injury has denied him that opportunity.
5.16pmOne area that Huddersfield may be looking to target United is at centre-back, where Chris Smalling has been shaky of late and Lindelof had a nightmare on his last trip to the John Smith's Stadium - his Premier League debut back in October in which the Terriers pulled off a shock 2-1 win.
5.18pmMourinho will hope that the extra protection of Carrick alongside Matic today will offer Lindelof greater protection. It is only the second time that the 36-year-old has started a match since September 2017.
5.20pmIt is interesting that Mourinho has lined up in a 4-3-3 formation, which is an option which has been mooted to get the best out of Pogba, whose suitability in a midfield two has been questioned.
5.22pmToday it is McTominay who gets the role on the right side of the midfield three. Carrick has been hyping up the youngster's potential this week, even tipping him as his own long-term successor.
He told MUTV: "I know he will take my place some day and that is not something I would be afraid of, or try to put him off, because it is important to help the future and Scott is definitely that."
5.24pmHEAD TO HEAD: Huddersfield have lost nine of their past 13 games against Manchester United, although their single victory did come at the John Smith's Stadium earlier this season.
5.26pmThis is the first FA Cup tie between the two sides in 55 years. United have won two of their three FA Cup ties against Huddersfield, most recently winning 5-0 in the third round in 1963.
5.28pmPREDICTION: With the lineup that Mourinho has named, I anticipate them having full control of the midfield and eventually grinding Huddersfield down. The hosts might get a goal though against a far from full strength United defence, so I will go for 2-1 to the Red Devils.
1 minKICKOFF: United get the action underway with the rain coming down in Yorkshire. The Huddersfield fans' spirits have not been dampened by the weather and are in good noise as always.
2 minQuaner gets in behind Shaw down the Huddersfield right. He sends the ball hopefully across goal but Tom Ince, whose father Paul played in two finals for United, is too far behind play to get on the end of it.
3 minGOAL! HUDDERSFIELD 0-1 MAN UNITED (ROMELU LUKAKU)
3 minIt is the perfect start for United as they score a very early goal which starts and finishes with great work from Lukaku. He holds the ball up and lays it off for Mata, before spinning off his marker and running onto a return pass. The Belgian holds off Christopher Schindler and turns back onto his right foot, before fooling Jonas Lossl with a cool finish to the near post with his right foot.
5 minThat goal is Lukaku's 19th of the season and means that he has now scored in three successive FA Cup rounds, having come off the bench to do so against Derby County and Yeovil Town.
6 minCHANCE! It has been a good response from Huddersfield, who create an opportunity for Ince through an excellent pass from Billing. It is a tight angle and the former Blackpool winger drags his effort across goal, with nobody gambling on a tap-in at the back post.
8 minYou would not know that Huddersfield have taken an early setback. Hadergjonaj gets forward from right-back and delivers an inviting ball towards Mounie which Lindelof heads out for a corner.
9 minBilling catches a left-footed shot really sweetly from 25 yards but Carrick is on hand to make a block, otherwise stand-in goalkeeper Romero would have had a job on his hands.
11 minFrom the corner which broke to Billing at the edge of the box, it did appear that the ball struck the hand of Smalling. Neil Swarbrick - the man on VAR tonight - might have felt there was a penalty in that for Huddersfield had Kevin Friend gone to the technology on that occasion.
13 minDavid Wagner will be really pleased with Huddersfield's reply to conceding that early goal. They have penned United back and prevented Mata or Sanchez from having a sniff of the ball.
15 minGood defending from Michael Carrick, who uses all of his experience to step in front of Quaner who had got beyond Shaw and into the area with the same knock it one way, run the other skill which I tormented defenders with for Wollaton Hall Green U10s.
18 minSanchez passes up a decent opening when he checks back onto his right foot to try to play a return pass to Lukaku, rather than drag the ball onto his left foot and attempt a shot from 20 yards.
20 minThe Red Devils have successfully slowed the game down in the last five minutes to prevent Huddersfield from increasing the momentum that they were threatening to build. Carrick and Mata are seeing a little bit more of the ball but United are being made to work very hard for every ounce of space.
21 minWilliams does well to get to the byline and stand a cross up for Van La Parra, but his header lacks any power and Romero catches with ease.
22 minHuddersfield storm forward again, and it is down the right flank which has been a great outlet for them in this opening 22 minutes. Hadergjonaj's cross is just in front of Ince who stretches out a foot in vein. Sanchez is giving Shaw absolutely no defensive support down the United left.
24 minMcTominay attempts an ambitious pass across field to Shaw which Quaner very nearly picks off. Had the German brought that under control, Huddersfield could have broken three-on-three.
26 minSmalling wins a header from a free kick but Lukaku is flagged offside from the knockdown.
28 minSHOT! Williams lines up a long-range shot which skips across the wet surface but into the arms of Romero, who takes it cleanly and is still yet to concede a goal in the competition this season.
30 minA poor clearance from Shaw gifts the ball to Quaner and Carrick is forced to concede a corner. Smalling and Lindelof get in each other's way at the near post but still clear the danger.
32 minInce exchanges a tidy one-two with Williams on the edge of the box but Matic prevents the winger, who has only scored twice this season, from getting a shot away on his left foot.
34 minSHOT! Billing certainly isn't shy of shooting from range and he gets some lovely shape behind a 30-yard hit with his left foot, but again it is straight down Romero's throat.
36 minThe Terriers threaten to counter down the left through Van La Parra and Kongolo, who is tripped by McTominay but is wrongly penalised for a foul of the young United midfielder.
38 minThere is a brief stoppage in play as Mounie receives treatment after a collision with Smalling. The striker isn't shy of a physical tussle so might give Smalling one back when he gets the chance.
40 minHadergjonaj is released again down the right but Lindelof cuts out his cross at the near post.
42 minVan La Parra bursts forward, exchanging a one-two with Mounie and earning a corner off Lindelof. Romero is off his line to punch clear with authority. While Huddersfield have been the better side in this first half, they have yet to really test the Argentine glovesman.
45 minDISALLOWED! United think they have taken a two-goal lead through Juan Mata, who rounds Lossl and slots home with aplomb from Young's slide-rule pass, but Kevin Friend refers an offside decision to VAR and Neil Swarbrick chalks the goal off!
45+2 minAccording to Graham Poll on BT Sport, the lines used to help the officials with offside decisions were not working and so Neil Swarbrick made the decision without the technology. Ay ay ay.
45+3 minDISALLOWED! United have another goal ruled out for offside, but the officials didn't need VAR to see that Matic was indeed beyond the last defender from Mata's free kick.
6.25pmKevin Friend gives himself and his fellow officials some respite with the half-time whistle, which brings to the end a really good 45 minutes of football marred by yet more VAR controversy.
6.27pmAlthough Huddersfield have been the better side, United can count themselves very unlucky to not have a two-goal lead. There was not clear evidence to rule Mata offside, therefore his goal should have stood. It was really well taken by the Spaniard, helped by some generous Terriers defending.
6.29pmAs it is, this cup tie is in the balance at the break, with the two sides only separated by Romelu Lukaku's 3rd-minute goal. Since then, the hosts have outplayed United at the John Smith's Stadium, without creating any clear-cut opportunities to test Sergio Romero and register an equaliser.
6.31pmNow journo Duncan Castles is so pro-United that he would tell you they've been the best team in Manchester this season, but he has a point here.
6.33pmHuddersfield boss David Wagner will be very pleased with how much control his side enjoyed during that first half, despite the absence of a couple of key midfielders. They were very dangerous down the right flank, with Sanchez either exempt from, or refusing to, offer Shaw defensive support.
6.35pmBENCH WATCH: Laurent Depoitre is the most obvious option off the bench for Huddersfield as they chase a goal in the second half. Sanchez has been ineffective and Martial may be an option to his the hosts on the counter, if they continue to have as much territory as they did before the interval.
46 minKICKOFF: The second half is underway, with both sides unchanged. Let's hope that this period provides us with enough action to make us forget about all that VAR nonsense.
48 minMcTominay ignores a good chance to play through Lukaku and Zanka comes across to quell the danger.
49 minHadergjonaj knocks the ball past Matic easily and Carrick has to be alert to intercept his cutback.
51 minInce wins Huddersfield a free kick on the edge of the box, with Shaw tripping the winger who steps up himself to take it but fires it into the wall. Van La Parra swipes the follow-up straight in the air.
53 minThe Terriers have another set piece on the edge of the box as Williams is fouled by Matic. Billings takes charge of the set piece but again the visiting wall stands tall and does its job.
55 minGOAL! HUDDERSFIELD 0-2 MAN UNITED (ROMELU LUKAKU)
55 minNo arguing with this one, as United hit Huddersfield with a slick counter attack which ends in a second to Lukaku. The Belgian shows good strength to hold off Zanka, work the ball onto his left foot and slot it under Lossl. The ball from Sanchez to set him free was absolutely fantastic too.
57 minThat goal might knock the stuffing out of Huddersfield, who were so good in the first half and started this second period on the front foot, but now have a huge mountain to climb.
59 minUnited suddenly look lethal on the break and it would not be a surprise if they soon get a third. On this occasion, Mata's pass is just too far ahead of Shaw and cut out by Schindler.
61 minMourinho's front three combine nicely to nearly open up Huddersfield again. Sanchez's crossfield ball is controlled on his chest by Lukaku, who slips in Mata on the overlap but the Spaniard has nobody in the box to help out and his square pass is picked up by Lossl.
63 minThe Red Devils have a big Champions League game against Sevilla in midweek. I wonder if that will come into Mourinho's thoughts in the next 10 minutes or so when he looks to his bench?
65 minHuddersfield won't give up on this match easily. They will feel hard done by to be 2-0 down, but they have allowed Lukaku a couple of chances and he has been super clinical with them both.
67 minInce ventures forward down the right but Shaw, who has had a tough evening, often left isolated by Sanchez, tackles strongly to halt his progress. United have defended well across the back four.
69 minSUBSTITUTIONS: Wagner makes a double change, deciding to swap both of his full-backs as Kongolo and Hadergjonaj come off for Malone and Smith. The Swiss has had a fine game but looks exhausted as he trudges off, so Wagner may be thinking fresh legs are needed.
71 minInce works the ball onto his right foot in the area but Smalling gets a block in. That is an important intervention from the England international as the shot was destined for the bottom corner.
73 minA good run and pull back from Young, found by Sanchez's through-ball presents Lukaku with a sniff of a hat-trick, but his right-footed shot from 20 yards is blocked by Schindler.
75 minSHOT! Billing has another pop from range which Romero holds at the second attempt. The Danish midfielder has been another standout performer for the hosts, and certainly packs a punch in that left foot. Romero has been equal to everything he has tried this evening.
77 minSUBSTITUTION: Mourinho brings off Sanchez for the final 15 minutes or so, bringing on Martial.
79 minMcTominay does some good defensive work backtracking to follow the run of Malone and prevent the substitute from getting onto the end of a pass by Billing. The homegrown midfielder hasn't stood out tonight but certainly hasn't looked out of his depth either.
81 minSUBSTITUTION: Jesse Lingard is on for the final salvos here, with Mata making way.
83 minLukaku might be snubbing the dabs and handshakes with Lingard in the dressing room at full time! Just on the pitch, the midfielder had a simple square pass on to set up Lukaku for an open goal and inevitable hat-trick, but dragged his ball behind the striker.
85 minSUBSTITUTION: Huddersfield's final change sees Abdelhamid Sabiri replace Van La Parra, and he is straight into the action with a header from a corner which is just off target.
87 minThis time it is Martial's comeback which fails to find either Lingard or Lukaku in the box. The former had gone to the near post, and Lukaku had hung back but the pass split them both.
89 minMounie, who has not had much service in the second half, sees his name up in lights when he tries an overhead kick from a Williams cross. The striker made contact, but barely.
90+2 minSUBSTITUTION: Lukaku gets a warm reception from the travelling fans as he exits the pitch, and they will be equally pleased to see the return of Eric Bailly after three months out.
7.28pmThe final whistle blows, signalling Manchester United's passage into the last eight of the FA Cup following a competitive tie with Huddersfield in which the clinical finishing of Romelu Lukaku was the major difference. Playing like that though, the Terriers have every chance of staying up this season.
7.30pmThat's it from Yorkshire, and you can read how United joined Chelsea, Southampton, Leicester and Brighton in the hat for the quarter-final with our match report here. The draw takes place before 8pm so stay tuned for Sports Mole to find out who your team get! Thanks for joining us today.