United were already leading through Mata's composed finish in the 14th minute at Anfield on Sunday when Gerrard made Liverpool's task even harder as he earned a red card just 43 seconds after coming on as a half-time substitute.
Making his final appearance against United before his close-season move to LA Galaxy, Gerrard was sent off, for the eighth time in his career, for a clear stamp on Ander Herrera.
United took full advantage of their numerical superiority as Mata scored a quite brilliant second goal in the 59th minute.
Angel di Maria picked out the former Chelsea midfielder with a clipped pass that Mata converted with a stunning bicycle kick.
Daniel Sturridge got one back for Liverpool 10 minutes later, but Brendan Rodgers' side couldn't find an equaliser, leaving Gerrard to apologise.
Fifth placed Liverpool are now five points behind fourth placed United.
"I have let my teammates and manager down today, even more importantly I let all the supporters down and I take full responsibility for my action," Gerrard said.
United's victory would have been even bigger if Wayne Rooney's stoppage-time penalty hadn't been saved by Simon Mignolet.
At the KC Stadium, Chelsea survived some self-inflicted wounds to secure a win that kept them firmly on course to win the title for the first time since 2010.
After second-placed Manchester City had closed to within three points on Saturday, the west Londoners are now six points clear again, with a game in hand making their position even stronger.
Jose Mourinho's side took just 78 seconds to go in front as Belgium midfielder Eden Hazard advanced to the edge of the penalty area, where he lashed a superb strike past Allan McGregor.
The Blues looked in complete control in the ninth minute when Spain striker Diego Costa cut in front the left to curl a fine finish into the far corner for his 19th league goal of the season.
But Hull reduced the deficit in the 26th minute thanks to Egypt international Ahmed Elmohamady, who swept home Andrew Robertson's cross from close range.
And Steve Bruce's team equalised just two minutes later after a disastrous piece of play from Chelsea goalkeeper Thibaut Courtois.
When Branislav Ivanovic pushed a risky backpass towards Courtois, the Belgian tried to take a touch before clearing, but he allowed the ball to trickle away from him towards Hernandez and the Uruguayan forward gratefully accepted the present as he slotted into the empty net for his first goal since October.
Courtois redeemed himself with a series of second half saves and Chelsea grabbed a priceless winner in the 77th minute when McGregor allowed a fairly tame shot from French forward Loic Remy, who had only been on for three minutes, to escape his grasp and trickle into the net.
At Loftus Road, Everton erased the frustration of their Europa League exit with a 2-1 success at lowly QPR.
Roberto Martinez's side had bowed out of Europe with a humbling 5-2 defeat at Dynamo Kiev on Thursday, but they took the lead in the 18th minute through Seamus Coleman.
QPR drew level when substitute Eduardo Vargas struck from close-range in the 65th minute.
But on-loan Tottenham winger Aaron Lennon won it for Everton in the 77th minute to move the Toffees nine points away from the relegation zone and leave second-bottom QPR four points from safety.