The Red Devils were home and dry before half time as Marcus Rashford's brace and a deflected strike from Jesse Lingard put them three goals up at the interval, before Anthony Martial added a fourth in the second half.
It looked as though it would be a fifth straight home win and clean sheet until Lloyd Dyer fired in a consolation for the visitors in stoppage time, although it was not enough to prevent the holders from cruising into the last 16.
Find out how all of the action unfolded courtesy of Sports Mole minute-by-minute coverage below.
The hosts are heavy favourites heading into this one, with a history which far outweighs the modest one of Burton and looking to rediscover their former glories this season. For Burton, though, the prospect of winning at Old Trafford could be the highlight of many of these players' careers, so they will certainly be up for this one.
Before we take a closer look at both sides, let's first check out the team news...
Well, it is no surprise to see a lot of changes made by Jose Mourinho this evening as he rests players for competitions of a higher priority, with the United boss making no fewer than nine alterations to the side which started the win over Everton at the weekend. Rashford and Mata are the only players to keep their place in the side for this evening's game.
The lineup released by the club suggests that Rashford will be given the opportunity to play through the middle in Lukaku's absence, having been forced to feature in the wider role so far this season.
Carrick played an integral role in United's season last term but is only expected to play a bit-part role this time around; Herrera, on the other hand, will have been hoping to be more involved than he has been so far. He has fallen down the pecking order since the arrival of Matic - and is seemingly behind Pogba, Matic and Fellaini now - but he gets his chance tonight.
Jones and Young are amongst the subs, though, alongside Luke Shaw who could be in line to make his first appearance of the season. The full-back has now recovered from injury, but his relationship with Mourinho still seems fraught following some public criticism last season.
As it happens, though, United have been one of the most impressive teams so far this term and come into this game level on both points and goal difference with local rivals Manchester City at the top of the Premier League table. It should be noted that United have had kinder fixtures to start the season than many of their rivals, but you can only beat what is put in front of you and so far United have done that to great effect.
One of the biggest problems last term was the number of dropped points at home - particularly via drawn games - but that is not an issue United have had so far this season with four wins from a possible four here at Old Trafford - all without conceding a single goal.
You have to go back more than a year for United's last home defeat in any competitions, a run which stretches 33 matches and includes 22 wins and 11 draws.
Since then the Red Devils have been knocked out at home twice on penalties and once via extra time, but they have won 15 of their last 18 EFL Cup outings in front of their own fans.
The hosts usually do get past at least this stage, though, reaching at least the fourth round in eight of the nine seasons - with the exception coming in that infamous 4-0 second-round defeat at the hands of MK Dons in 2014-15.
The 3-2 victory over Southampton at Wembley handed Mourinho his first major piece of silverware as manager of the club, and repeating the feat this season would see them become the first team to retain the trophy since they themselves did it in 2009 and 2010.
This is, of course, another level up from that entirely, so not many will be expecting Burton to threaten an upset tonight.
Burton were still a non-league side less than a decade ago, so it has been a pretty rapid rise to their level at the moment and they will just be enjoying it while it lasts right now.
Having lost all of their opening three Championship outings, Burton have since beaten Birmingham and Fulham as well as drawing with Sheffield Wednesday and Norwich - the latter three of whom are all expected to challenge for the playoffs this season. There was a 5-0 defeat to Leeds in the midst of all that, but that is their only loss in their last six outings.
The concern for Clough will be that his side's goal difference has been poor so far, with only bottom club Bolton having conceded more and only the bottom two - Bolton and Birmingham - having scored fewer.
The reward of a trip to Old Trafford will, of course, make that all worthwhile, and anything extra tonight will just be a bonus for the visitors.
It is a different story in the EFL Cup where Burton have won their last four away games and have not been beaten on the road in normal time since a 5-1 defeat at the hands of Reading in August 2009.
Burton's most recent EFL Cup game against Premier League opposition saw them swept aside by Liverpool, though, as Klopp's side ran out 5-0 winners in the second round last season.
There only looks like being one winner tonight - United have named a weakened starting XI as expected, but there are still plenty of players in there who would not look out of place in a Mourinho team to start a Premier League game, so they should have enough to see them through here. A comfortable home win on the cards!
Sports Mole says: Manchester United 3-0 Burton Albion
MAN UTD STARTING XI: Romero; Darmian, Lindelof, Smalling, Blind; Carrick, Herrera, Lingard, Mata, Martial; Rashford
BURTON STARTING XI: Ripley; Flanagan, Turner, Naylor, Lund, Dyer, Allen, Palmer, Mason, Varney, Akpan
Carrick fires a pacey low pass into the feet of Lingard inside the area, and the United midfielder produces a lovely touch to poke the ball away from a defender and tee up Rashford. The striker at first doesn't seem to read it, but he is quick on to it and dinks a cool finish past the keeper.
It is Rashford who does the damage again, this time from dropping deep and firing a pinpoint finish in off the post. The striker was given too much space, but he still had a lot to do when he collected the ball 25 yards from goal. He only had one thought in his mind, though, spinning on the ball and firing an effort past the keeper and in off the woodwork. Clinical.
4 - Marcus Rashford has now scored four braces for Man Utd, with each one coming in a different competition. Range. pic.twitter.com/zkOdAPoHCw— OptaJoe (@OptaJoe) September 20, 2017
Rashford is again involved in the buildup, playing the ball to Martial who in turn drives forward before giving it on to Lingard. There is a huge element of luck about it as Lingard's effort takes a major deflection off the leg of Burton, sending the keeper the wrong way and nestling into the corner.
Lingard feeds the ball to the feet of the Frenchman, who flicks it on towards Rashford. Turner should cut it out, but he misses his kick and Rashford is onto it as quick as a flash. He plays the ball into the path of Martiak, who continues his run, and the winger makes no mistake with only the keeper to beat.
The match was over as a contest by half time, though, with Rashford scoring a brace and Lingard adding a third in the opening 45 minutes to leave the holders in complete control. Martial then got in on the act in the second half, and the only blemish on United's performance tonight was that late strike from Dyer.