Livermore's first Hull goal put the home side in front after 20 minutes at the KC Stadium on Sunday, but a superb Steven Gerrard free-kick almost 15 years to the day since his Liverpool debut levelled matters.
But Hull were rewarded for a stirring second-half performance when Meyler reacted quickest to pick up the loose ball and fire in with 19 minutes remaining before Martin Skrtel's own goal settled matters.
The result catapults Hull into the top half of the table and leaves Liverpool seven points adrift of Premier League leaders Arsenal.
Hull manager Steve Bruce made two changes from last weekend's defeat to Crystal Palace and Liverpool counterpart Brendan Rodgers made three alterations following the 3-3 Merseyside derby draw.
Philippe Coutinho opened the scoring against Everton last Saturday but was one of those who dropped to the bench, while the injured Paul McShane was replaced by Alex Bruce for Hull.
Bruce's men had lost four of their previous five Premier League games and despite Liverpool's dominance of possession, it was the home side who created the first chance.
A corner was cleared as far as Bruce after 14 minutes and his teasing cross was glanced just wide by Curtis Davies.
And Hull went in front six minutes later when Livermore and Meyler combined for the former to unleash a shot that took a wicked deflection off Skrtel and flew past Simon Mignolet, his first goal for the club since joining on loan from Tottenham.
But the lead was short-lived as Liverpool captain Gerrard produced a sumptuous free-kick that he whipped into Allan McGregor's far corner from 25 yards.
Luis Suarez cut a frustrated figure for most of the half and he missed a very presentable opportunity in the final minute of the opening period when Raheem Sterling found the Uruguayan on the left, but his side-foot effort was tame and straight at McGregor.
Liverpool should have gone in front after 70 minutes when Coutinho's cross found Victor Moses, who met it on the volley but was denied at point-blank range by McGregor.
McGregor's save proved crucial as Hull regained the lead a minute later after Liverpool failed to clear and Meyler picked up the loose ball and showed great composure before firing in his first goal of the season.
Suarez whistled a late free-kick wide before Hull put the game out of reach with four minutes remaining when Huddlestone's effort was headed into his own net by the unfortunate Skrtel.
