The Reds were without the prolific Daniel Sturridge as he began what could be a stint of up to eight weeks on the sidelines after suffering ankle ligament damage in training on Friday.
Rodgers had recalled Victor Moses and Raheem Sterling, the latter making his first start since October 5, but they proved inadequate replacements for Sturridge and Liverpool's consolation, a first-half equaliser, came from the more reliable source of a Steven Gerrard free-kick.
Hull had gone ahead through Livermore's first of the season, via another Skrtel deflection, and took a deserved lead when Meyler buried a low shot in the 72nd minute.
Rodgers side lost all sense of shape as they attempted to retrieve the game and conceded a third when Tom Huddlestone's off-target effort was nodded home by Skrtel.
For Hull, it was a memorable afternoon and a season's best performance - just the boost required after last week's defeat to lowly Crystal Palace.
Hull had started the day by digesting another round of inflammatory comments from owner Assem Allam.
His proposals to rebrand the club as Hull Tigers led to the formation of an opposing "City Till We Die" fans' group and Allam told a Sunday newspaper that members of it could "die as soon as they want".
With the match just a couple of minutes old supporters in the East Stand gave their response, chanting: "We're Hull City, we'll die when we want."
The match itself quickly settled into a pattern of Liverpool going forward and Hull clearing their lines.
The Reds forced three corners in the first six minutes, but the hosts stood up well to Gerrard's delivery.
There were hints that Hull were not going to be completely passive, though, Yannick Sagbo and Livermore creating a promising counter-attack in the 14th minute only for Robert Koren to linger too long over a final ball.
Nevertheless, it was still a major surprise when Hull went ahead six minutes later.
Moses was culpable, giving the ball away to Ahmed Elmohamady when trying to attack from the back and bringing Livermore into the game.
He exchanged a quick one-two with Meyler, advanced on goal and saw his 20-yard strike loop past Simon Mignolet via a heavy deflection off Skrtel.
Hull's game plan would surely have been to grit it out until half-time with their lead intact but with 26 minutes gone Curtis Davies felled the advancing Jordan Henderson and offered Liverpool the most inviting of free-kicks.
Luis Suarez appeared interested but Gerrard pulled rank. It was a decision he would not regret, bending the ball brilliantly past Allan McGregor after Skrtel pulled away from the wall to create a gap for the shot.
The leveller settled Liverpool and both Gerrard and Suarez began to play with greater freedom as they probed Hull for further openings.
Yet they did not muster a shot of note between them until the stroke of half-time when Suarez hit an unusually tame effort from Sterling's clever through ball.
Moments earlier Hull winger Robbie Brady was booked for diving as he tumbled in the penalty area despite Lucas Leiva making no apparent contact.
Liverpool started the second period shakily, Kolo Toure at times resembling an accident waiting to happen at the back.
The impetus was still on them to win the game but Moses and Sterling were offering little cutting edge in support of Suarez.
Hull threatened on the hour when Davies headed a Brady free-kick a yard wide of Mignolet's goal and the momentum began to tilt in the home side's favour.
Huddlestone almost capped an impressive performance with a neat touch and shot from the edge of the area and Hull pressed home their advantage at the next attempt.
Meyler was the scorer, driving into the bottom corner after his initial strike was blocked by Toure, but Davies, Sagbo and Livermore all had a hand in the build-up.
Just before the goal McGregor made a brave close-range save to deny Moses, a contribution just as vital to the cause.
Liverpool went to pieces in the last 15 minutes, frequently leaving themselves exposed as they threw numbers forward.
A third goal seemed inevitable and came when Sagbo met a hopeful punt from the back and held the ball up long enough for Huddlestone to arrive in the box.
His chance to finally end a long goal drought - and go for the haircut he has promised to have when he next scores - was not taken as his shot looked to be heading well wide until Skrtel intervened and left Mignolet stranded.