The recalled playmaker's intelligent finish shortly after the break settled the 173rd Manchester derby and ensured a modicum of revenge for last month's league defeat.
We progressed to the last eight to face West Ham after a much needed and confidence boosting win that restored belief and a sense of pride to all those in Red following Sunday's debacle.
As a result of that defeat, Mourinho named a stronger side than perhaps we expected, while, in contrast City boss Pep Guardiola fulfilled his promise to rotate.
Despite a much-changed side, however, the visitors started in a menacing mood and could- maybe should- have gone ahead inside five minutes.
Kelechi Iheanacho scored in the league encounter last month and almost did so again here when he steered a header narrowly off target after Jesus Navas had picked him out.
Aleix Garcia had a possible penalty appeal turned down when he went down under a challenge from Michael Carrick but referee Mike Dean waved play on.
Zlatan went close with a free-kick and then had an effort deflected over the top by Nicolas Otamendi after Marcus Rashford had linked up well with Luke Shaw.
Iheanacho and Antonio Valencia were both booked for strong challengers before Marcos Rojo blocked superbly from Leroy Sane after Daley Blind was caught in possession.
Neither goalkeeper had much to do in the first half but Willy Caballero was soon called into action as United came flying out of the traps after the restart.
The City stopper made a stunning save to push Paul Pogba's effort onto a post after Zlatan had played him in.
The Reds continued to press and got what turned out to be the decisive goal nine minutes into the half.
The impressive Zlatan's cutback evaded the onrushing Ander Herrera- who collided with Fernando amid screams for a penalty- but the ball broke for Mata to steer in from close range.
Old Trafford erupted but City were not going quietly and introduced big guns Raheem Sterling and Sergio Aguero to try and turn the tie around.
Aleksandr Kolarov fired over with a 25-yard free-kick, Rashford shot wide and Caballero did well to deny Pogba when clean through.
City probed for a leveller but they were unable to find a way through- or even a shot on target- and the Reds held out to deservedly earn a quarter final place.
We return to league action with the visit of Burnley and will take confidence and satisfaction from sending the neighbours packing at the end of a testing ten days.
Up the Reds!
Overall team performance: 8.5/10
United Faithful Man of the Match: Juan- nil, Juan Mata.