The striker's goal came in the first minute of the second half after he lost his marker Jose Enrique and slotted home Wayne Rooney's corner from close range.
Shinji Kagawa and Suarez saw efforts hit the crossbar as United held on to make the fourth-round draw, where they will play Norwich at home.
Suarez was in the Liverpool starting line-up after completing his ten-game ban for biting Branislav Ivanovic last season, with manager Brendan Rodgers recalling the Uruguay forward at the first available opportunity.
Indeed, there was no resting players for this competition, with Steven Gerrard and Daniel Sturridge also included in a full-strength Reds line-up.
Meanwhile, Rooney captained a strong United side that nevertheless showed eight changes from the team defeated 4-1 at Manchester City on Sunday.
David De Gea also kept his place but Wilfried Zaha and Adnan Januzaj were only on the bench as Javier Hernandez and Shinji Kagawa were amongst those to start for David Moyes.
It was hardly a surprise Suarez should start.
After all, when you have spent so long out and are desperately in need of match fitness, there is little to be gained by kicking your heels on the bench watching others do what you are paid so much for.
Perhaps understandably though, the Uruguayan was not quite on top form.
He was caught on his heels slightly when Steven Gerrard rolled an inviting pass into his path, which allowed Rafael to slide back and clear.
And when Enrique's curling cross dropped over Jonny Evans' head, Suarez's first touch was just too long so De Gea was able to slide out to bravely block his second.
He did supply the through ball that ended with Sturridge toe-poking wide.
Suarez would have also got the assist if Victor Moses had been able to drill hisquare ball home. Moses didn't get the opportunity though as Ryan Giggs reached it first.
It was all part of an absorbing opening period, notable for the fact neither goalkeeper actually had a shot to save.
As befitting a team that got so badly beaten at the weekend, and containing so many players with so much to prove, United started with intent.
Nani and Kagawa were particularly lively, whilst stand-in captain Rooney buzzed around with menace.
However, with the exception of a Nani effort that was deflected wide, all that early pressure fizzled out and it wasn't until much later in the half United started to force the pace again.
Some kind of relief was required. And it arrived through Hernandez's goal a minute after the re-start. Indeed, the Mexican's first goal of the campaign came so early in the second half, United manager Moyes had barely got beyond the penalty area in his walk to the home dug-out.
It meant it was easy to spot the Scot's celebration, at a strike that should at least quell some of the angst that built up following that awful hammering at City four days ago.
But United's performance was far from perfect. Indeed, De Gea produced a fine reaction save to repel Moses' powerful diving header.
Suarez then came close to levelling when his vicious free-kick struck the bar after a slight Phil Jones deflection with De Gea beaten.
But the hosts had chances to sew up the contest too, with Simon Mignolet producing a couple of excellent saves to deny Rooney, while Kagawa glanced the crossbar with a long range effort.
And, after bravely riding the hefty punches landed on him at the Etihad Stadium, Moyes was left to celebrate a much-needed victory against one of England's biggest clubs, and United's greatest rivals.