The in-form Spanish playmaker scored the vital third goal after 67 minutes, with Ashley Young and Marouane Fellaini having cancelled out Sergio Aguero's early opener.
Chris Smalling added the final United goal before Aguero reached 100 goals for City in anti-climactic fashion.
After the game Mata urged his team-mates to fight to secure a UEFA Champions League qualification spot they are strong favourites to claim.
"In the first 10 or 15 minutes City were brilliant, but after that we showed character and came back," he told Sky Sports.
"It was a massive result and everyone from United is happy.
"The atmosphere was crazy, it's something we will never forget. We have six games to go and have to keep going."
United are now four points clear of City in four and a solitary point behind second-placed Arsenal.
"It's one more step towards the Champions League, it's a big win and a boost to the confidence," Mata added.
"But Arsenal are a great team and City and Liverpool will stay fighting until the end."
