An entirely different starting XI to the side thrashed 6-1 on Sunday by Manchester City made sure there was no hangover thanks to Dimitar Berbatov and Antonio Valencia's first goals of the season and another competition strike from Michael Owen at the EBB Stadium.
Aldershot tried their best to bridge the gulf in class between League Two also-rans and the Premier League champions, but they failed until late on to seriously test a rearguard that had looked vulnerable in the extreme in recent weeks.
United arrived in Aldershot to witness a town buzzing for the club's biggest game since they reformed in 1992 following the demise of Aldershot FC, and one of the biggest since the latter hosted a star-studded United team in the same competition 41 years earlier.
Their 7,300-capacity ground was full to bursting and the home fans arrived hoping to see one of the biggest shocks in League Cup history against a side who had never lost to a club from the fourth tier of English football.
United had also not suffered as bad a derby defeat as City inflicted on them in 85 years, a result manager Sir Alex Ferguson branded the worst of his entire career.
Dean Holdsworth's Shots were looking to compound his misery and there were a few minor scares early on as the visitors gave the ball away in midfield.
But United soon took charge and Tom Cleverley, back after six weeks out with a foot injury, curled over the bar from 20 yards.
Returning captain Nemanja Vidic was booked for felling Alex Rodman in the 10th minute but that was a false dawn for the home side as the visitors showcased their superior class five minutes later.
Park Ji-sung played a one-two with Cleverley on the edge of the box before finding Dimitar Berbatov, who passed the lay-off into the net.
The home fans responded with chants of "We're going to win 6-1", which looked optimistic when Fabio dragged wide and Luke Guttridge was forced to clear Berbatov's knock-down from in front of goal.
But Aldershot almost levelled through a superb solo effort from the dangerous Jermaine McGlashan, who ran at the heart of United's defence before unleashing a rising drive that just cleared the crossbar.
Berbatov and Mame Diouf both powered headers over under pressure before Michael Rankine failed to make the most of a free header from a corner and Danny Hylton sent a turn and shot straight at Ben Amos from a tight angle.
That was in the 41st minute and United immediately broke down the right with Berbatov squaring for Owen, whose shot straight down the middle managed to beat Ross Worner for his third goal in two League Cup ties this season.
Rodman failed to emerge for the second half after taking a knock to the shoulder towards the end of the first, with Bradley Bubb coming on.
The contest was over three minutes later as United scored with the first attack of the half, a 20-yard Antonio Valencia piledriver leaving Worner clutching air.
Aldershot looked determined to salvage some pride but that left them wide open on the counter and Berbatov dragged wide when he really should have made it 4-0.
Cleverley's comeback lasted just short of an hour as United brought on Paul Pogba, who was joined on the field by Ravel Morrison and Michael Keane 10 minutes later, Diouf and Ezekiel Fryers being replaced.
Aldershot introduced Jamie Collins for Peter Vincenti, while their fans continued to give as good as they got in the banter stakes with the small pocket of United supporters.
With 10 minutes remaining, Worner produced arguably the only world-class moment of Aldershot's night with a sensational save from Berbatov's 20-yard free-kick.
Adam Smith came on for Rankine and a late rally saw Guttridge drill inches wide and force a brilliant stop from Amos with a curling free-kick before Valencia blazed over when clean through on the break.