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.
The hosts finally got their third goal with 17 minutes remaining as Wilson squirmed away from his marker before firing low past Dunn from the edge of the penalty area.
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.
After causing problems for the Manchester United defence in their first meeting, Cambridge were immediately on the attack at Old Trafford and should have been ahead inside the opening minute.
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.
Cambridge were made to rue that miss as Manchester United quickly took control.
Wayne Rooney wasted two early chances to beat Dunn, but the pressure eventually told midway through the first half when Mata ended 115 goalless minutes between the two sides.
The Spaniard was perfectly placed to convert Marouane Fellaini's knock-down after 25 minutes, following a deep cross from Angel di Maria.
And the lead was doubled within seven minutes, Rojo rising at the near post to head home an exquisite chipped pass from Van Persie for his first Manchester United goal.
Cambridge appeared to be sinking fast, but the League Two side showed they were still able to pose a threat when Ryan Donaldson dragged an effort wide before the break.
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.
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