The former Crystal Palace attacker was the difference between the two sides in a lively match at Leigh Sports Village
Chances came and went in the first half as goalkeepers Matty Urwin and Sam Johnstone maintained the stalemate, but once Zaha opened the scoring on 67 minutes there was only going to be one winner.
Zaha, who had been thwarted numerous times, eventually broke the deadlock, exchanging passes with Fabio da Silva before firing home from close range.
Nine minutes later and United added a second, James Wilson finding the corner of the net with a 20yd free-kick after Zaha had been felled.
The visitors could have scored further goals, but excellent saves from Urwin saw Rothwell and Pereira denied at the death.
Rovers worked hard throughout, showing excellent battling qualities, but they just lacked that incisiveness in the final third.
Darren Fletcher and Wilfred Zaha linked up well early on, but it was Rovers with the first effort on goal.
Following Hugo Fernandez's tackle on Zaha, Jordan Slew broke from inside his own half, racing to the edge of the opposition area before shooting left-footed, but Sam Johnstone in the United goal turned the effort behind.
Just past the midway point of the half an error from Matthew Urwin almost proved costly. The Rovers goalkeeper was quick to release the ball but could only throw it as far as Joe Rothwell. The United midfielder teed up James Wilson but Urwin redeemed himself by saving the effort with his legs.
Play then went straight up the other end as the pace of Slew again caused problems, he found Jordan Preston in the area but he couldn't get a clean connection to his shot and Johnstone claimed.
As the half wore on the visitors grew in the ascendency, a vicious shot from Zaha was headed clear by Fernandez before a ball over the Rovers back line saw Rothwell through but his first touch allowed Urwin to claim.
Raheem Hanley forced a save from Johnstone after good work from Preston, whilst quick feet from Zaha saw space open up, however Urwin was equal to the England man's efforts.
Manchester United should have broken the deadlock on the stroke of half-time, James Wilson turning well in the area to shoot across goal but Urwin got a vital touch to prevent the ball finding the net.
It was an entertaining first 45, the only thing lacking was a goal.
Rovers made a change at the start of the second half as one Academy striker replaced another, Dean Rittenberg on for Jordan Preston, but it was United who started the stronger of the two sides.
A deflected shot from Fabio crept a yard over Urwin's bar before a twisting Zaha could only find the side netting.
Then a racing Rittenberg looked to find Tim Payne in the area but Johnstone claimed well.
Zaha continued to pose questions of the Rovers' defence, a superb volley on 66 minutes kept out by an equally impressive save by Urwin, but a minute later the Rovers resolve was broken.
Inevitably it would be Zaha, the former Crystal Palace man exchanging passes with Fabio da Silva before sliding the ball under the advancing Urwin.
Zaha would have a hand in United's second goal on the night, his trickery resulting in a lunging foul from Kellen Daly. James Wilson took the 20yd free-kick and fired it hard and low under the wall and into the corner of the net wrong-footing Urwin.
Rovers maintained their work ethic until the final whistle but they couldn't get their reward of a goal.
ROVERS: Urwin, Fernandez, Olsson (sub Bauress 64 mins), Lenihan (sub Cotton 79 mins), Daly, Songo'o, Slew, O'Sullivan, Preston (sub Rittenberg 46 mins), Payne, R. Hanley.
Subs not used: Raya (GK), Haley.
MAN UTD: Johnstone, Varela, James, Rothwell, Ekangamene, Thorpe, Janko (sub Pearson 69 mins), Fletcher, Wilson (sub Pereira 79 mins), Fabio, Zaha.
Subs not used: Gollini (GK), Love, Rudge.
Goals: Zaha 67 mins, Wilson 76 mins.