Goals from Juan Mata, Marcos Rojo and substitute James Wilson were enough to seal a place in the next round for the 11-time winners, who had been surprisingly held to a goalless draw by Cambridge in the initial tie.
Having survived a scare in the first minute when their League Two opponents hit the post, Louis van Gaal's side quickly found their stride as Mata and Rojo both converted from close-range prior to half-time.
Robin van Persie had a trio of chances to add to Cambridge's misery early in the second half, but goalkeeper Chris Dunn kept him at bay with his alert reactions.
Manchester United will now travel to Deepdale in the fifth round after Preston North End came from behind to beat Sheffield United 3-1 in their replay on Tuesday.
A mistake from Daley Blind inside the hosts' half gifted the ball to Tom Elliott and the striker raced away from Chris Smalling but saw his curling effort clip the outside of David de Gea's left-hand post.
The Spaniard was perfectly placed to convert Marouane Fellaini's knock-down after 25 minutes, following a deep cross from Angel di Maria.
Van Persie should have extended his team's lead in the opening five minutes of the second half as Paddy McNair lofted a cross to the back post, but the striker could not direct his header on target.
Dunn then denied the Netherlands international on two occasions as the hosts camped on the edge of Cambridge's penalty area.
Van Persie was replaced soon after and the man who took his place, Wilson, grabbed Manchester United's third after 73 minutes, the youngster's low shot bouncing in front of Dunn on its way to the bottom-right corner.
Rooney's attempts to net his first FA Cup goal of the season continued in the closing minutes, but he finished goalless as a late curling effort from 20 yards drifted inches wide.
