The Reds winger, who joined the Bluebirds for the remainder of the season on Friday, came off the bench on 38 minutes and made a near-immediate impact.
Shortly after the break, Zaha set up Craig Bellamy to level the scores, before Kenwyne Jones scored what proved to be the winner a minute.
Although victory for Ole Gunnar Solskjaer's men was not enough to take them out of the relegation zone, just three points now separate them from 12th place.
Elsewhere, Federico Macheda scored a last-gasp equaliser for Birmingham City, as they held Derby to a 3-3 draw at St. Andrews in the Championship. The striker, making his first appearance for the club, was introduced on the hour mark and fired home from close range with the last kick of the game.
Defenders Tyler Blackett and Tom Thorpe also started the game for the Blues after completing six-month and four-week loans to the Midlands respectively. Blackett played a full match for Lee Clark's side, while Thorpe suffered an unfortunate early injury and was stretchered from the pitch.