It could have been 4-0 before half-time but De Gea produced another great save to deny Adam Lallana as United were lucky to head into half-time only a goal down.
United changed to a three at the back ayer the break, but Liverpool continued to be in the ascendency, with Coutinho forcing De Gea into yet another great save from distance.
Liverpool were in complete control, and Clyne almost doubled their lead, but De Gea, punched away his 25 yard strike.
Jordan Henderson was next to go close, but his first time shot went just wide of the post, and it looked like the Reds wouldn’t get a deserved second.
But they were rewarded for their brilliant display when Carrick’s woeful defending allowed Lallana to set up Firmino, who fired home from close range to seal the win.