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A lacklustre game at Old Trafford was drifting towards a goalless draw when Mata collected a pass from Oscar and dispatched a low shot that took a slight deflection off Phil Jones on its way into the bottom-right corner.
Mata's goal means that Chelsea will now go into Wednesday's crunch clash against Tottenham Hotspur at Stamford Bridge with a three-point lead over their London rivals, who are bidding to crash into the top four.
Arsenal are sandwiched between the pair in fourth, a point behind Chelsea, having played a game more.
United had right-back Rafael da Silva sent off late on and although their lead over second-place Manchester City remains 13 points, they have failed to win in two games since clinching their 20th league title.
United made five changes from the side that drew 1-1 at Arsenal last weekend, with Rio Ferdinand, Wayne Rooney and goalkeeper David de Gea among the players dropping to the bench.
Chelsea were missing Eden Hazard due to a calf strain and made four changes from their Europa League semi-final second leg success against FC Basel on Thursday.
The visitors made a bright start, with United goalkeeper Anders Lindegaard touching a shot from Oscar onto the post and Demba Ba curling a shot wide from the left.
United came to life slowly and did not pose a threat until late in the first half, with Robin van Persie diverting a glorious Ryan Giggs pass wide and then heading straight at Petr Cech from Nemanja Vidic's cross.
The second half was similarly underwhelming, with Frank Lampard blazing over for Chelsea and United substitute Rooney heading over the bar at the other end.
Mata finally settled things with three minutes to play with a low shot that nicked off Jones and trundled past Lindegaard, before Rafael was sent off for kicking out at countryman David Luiz.
Everton remain on course to finish above Liverpool for the second season in a row after holding their city rivals to a 0-0 draw in a scrappy Merseyside derby at Anfield earlier in the day.
Liverpool's best chance saw a goal-bound effort from man-of-the-match Steven Gerrard cleared by Everton defender Sylvain Distin, who had a goal controversially disallowed at the other end.
It meant Liverpool stalwart Jamie Carragher failed to finish on the winning side in his 30th and final Merseyside derby, while Everton are still without an away win in this fixture since 1999.
The draw left Everton somewhat marooned in sixth place in the table, five points above their neighbours and five points below the European qualifying positions with two games to play.
"I don't want to be a whinging manager, but we scored a legitimate goal today. It should have counted," said Everton manager David Moyes.
"We're still in there - we picked up a point again today. We've got two games to go and we'll keep pushing to try to get in there (the top five) if we can."
Gerrard thought he had put Liverpool ahead in the second half, but after rounding visiting goalkeeper Tim Howard, he saw his shot cleared off the line by Distin.
Distin had earlier seen a header ruled out by referee Michael Oliver for a foul that was far from evident, but Liverpool manager Brendan Rodgers felt defeat would have been harsh on his side.
"I can have no complaints," he said. "The players gave everything and the very least we deserved was a point."
