Jesse Lingard scored twice for holders United as the much changed Reds progressed to the Carabao Cup quarter finals.
It was a dominant and solid response from Saturday's Huddersfield horror show, with Sergio Romero only tested in stoppage time.
Jose Mourinho had ripped into the team after the loss in Yorkshire and made seven changes from that line-up, including Academy graduates Axel Tuanzebe and Scott McTominay.
United started strongly and went close early on through Chris Smalling, who headed over the bar from a Marcus Rashford corner.
Stand-in Swans stopper Kristoffer Nordtfeldt then saved well from Lingard, but it was he who put United ahead on 21 minutes.
Ander Herrera played the ball in to Rashford, whom in turn found his England colleague with a neat reverse pass, and Lingard did the rest with a well-taken finish beyond Nordfeldt.
Victor Lindelof blocked well from Wayne Routledge when he found himself one-on-one, and there was danger again soon afterwards for the visitors.
Daley Blind's deflected clearing header spun off Oliver McBurnie and wrong-footed Romero, but the ball rolled narrowly wide of the post with the keeper beaten.
McTominay went close from distance with a 25-yarder at the other end shortly before the interval.
United had soon put the result beyond any lingering doubt, however, when we moved 2-0 ahead on the hour mark.
At the culmination of a superb, sweeping team move that involved six players, Matteo Darmian picked out Lingard and he headed home from eight yards for his third goal of the season.
Like McTominay, Tuanzebe went close to a first United goal when he was denied by a smart stop by Nordfeldt and then fired the loose ball over the bar on the rebound.
Swansea introduced Tammy Abraham on 72 minutes, and the striker almost made an instant impact within minutes of coming on.
Romero had been a virtual spectator but was finally called into action as he tipped behind Abraham's speculative 25-yard strike.
The hat-trick hunting Lingard fired wide and then volleyed a second effort straight at the keeper, but the Reds had done more than enough.
Romero saved superbly from Leroy Fer in the dying minutes, but the Reds had done more than enough to ensure safe passage into the last eight.
Teenage striker Edward Nketiah came off the bench and scored twice as Arsenal beat Norwich, whilst City squeaked past Championship leaders Wolves on penalties to also go through.
Chelsea host Everton on Wednesday with the draw for the quarter-finals to follow.
Overall team performance: 7.5/10
United Faithful Man of the Match: Jesse Lingard. Scored two excellent goals and proved a thorn in Swansea's side throughout.