Sir Alex Ferguson's men bounced back from their 6-1 Premier League defeat at the hands of Roberto Mancini's charges in October to progress to the fourth round of the famous competition in wet conditions on the blue side of Manchester.
Wayne Rooney netted a double for the victors, who skipped away to a three-goal lead, before a courageous City - who were reduced to ten men when captain Vincent Kompany was dubiously sent off in the 12th minute - came back with two second-half goals but were eventually eliminated from the competition they triumphed in last season.
United blew off some cobwebs inside ten minutes when Rooney played a wide pass out to Antonio Valencia down the right with the Ecuadorian sending the ball into the area for the Red Devils striker to score into Costel Pantilimon's top right corner with a brilliant header.
City went a man down two minutes after the opening goal when Kompany came through with a two-footed challenge on Nani with referee Chris For brandishing a straight red which was questionable as he failed to make contact with the Portuguese winger.
The one-man advantage was put to good use by United who scored a second on the half-hour mark when Nani released Patrice Evra down the left with the French veteran sliding it towards Danny Welbeck whose first touch popped up onto the head of Samir Nasri but the United striker was able to turn and hit a sweet volley to Pantilimon's left and into the back of the net.
Less than ten minutes later, United were three to the good when Aleksandar Kolarov chopped down Welbeck in the area with Foy pointing to the spot. Rooney took honours and although his spot-kick was brilliantly saved by Pantilimon, the ball bounced perfectly into the path of the England ace and he was able to nod home unchallenged from close range.
Early in the second half, City struck back when Kolarov atoned for his earlier foul by hitting a brilliant curling free-kick over the United wall and into Anders Lindegaard's top left corner to put some spice back into proceedings.
A few minutes after the re-introduction of Paul Scholes, who came out of retirement earlier in the day, City were back within a goal in the 64th minute when the veteran midfielder gave it away with a sloppy pass on the right flank. James Milner was the recipient and managed to wriggle himself free to send a perfect cross into Sergio Aguero who hit a first-time shot which was saved by Lindegaard but the Argentine was able to react quickest and finish the rebound from right near the goal-line, sending the home fans into raptures.
Other notable chances included Lindegaard coming up with a massive save in the 14th minute when Aguero put a dangerous curling effort from range on target before Welbeck was inches away from toe-poking Valencia's whipped cross from the right past Pantilimon late in the first half.
In the 73rd minute, Scholes tested Pantilimon with one of his customary well-struck, low drives less than ten minutes before City had shouts for a penalty when Kolarov's low cross bounced up off Phil Jones' knee and onto his arm but referee Foy waved away the protests.
City had a late chance to grab a leveler when Kolarov hit a curling free-kick on target only to see Lindegaard make a fumbled, nevertheless, vital save before Kolarov's later corner was met by keeper Pantilimon whose header went wide as the home side acted desperately to tie up the encounter but in the end were unable to do so as United ended a two-game losing streak.
FA Cup third round
Etihad Stadium, Manchester
Rd card:MANC - Vincent Kompany 12'