West Brom goalkeeper Ben Foster included a Steven Gerrard penalty among a string of saves which laid the platform for the Baggies to record their first league win since Boxing Day.
The former England international denied the Liverpool captain twice, once from the spot, Jordan Henderson, Daniel Agger, Stewart Downing and Fabio Borini.
And when Gareth McAuley headed home West Brom's first effort on target in the 81st minute it set up their first league double over the Reds - having won 3-0 on the opening day of the season - since 1966-67, with substitute Romelu Lukaku's 90th-minute striking giving the scoreline an unbalanced look.
All the promise of performances in draws against Arsenal and Manchester City was wiped away in 90 torturous minutes as Liverpool suffered their first home defeat since mid-December.
West Brom are not supposed to like Mondays. They had not won any of their previous 18 top-flight away matches on this day, a run stretching back 44 years to March 1969.
However, they appeared more than comfortable in a disappointing first half which saw both teams manage just two shots on target between them.
Both of those were registered by the hosts as the Baggies were not intent on showing much adventure but with Liverpool not clicking into any sort of gear they were not in much danger either.
With Daniel Sturridge's thigh problem not being risked the Reds were shorn of the pacy, incisive running which caused the Premier League champions so many problems in the 2-2 draw at the Etihad Stadium.
Replacement Jonjo Shelvey was given his first league appearance since Boxing Day, playing in the hole as Luis Suarez was restored to the out-and-out striker role but he pair failed to get in the way Sturridge has.
The 20-year-old did put the ball in the net early on but was well offside, which sort of set the tone for the half which was briefly enlivened by Suarez producing a brilliant behind-the-leg cross.
Agger had a header tipped over by Foster, who also caught Stewart Downing's stinging drive at the second attempt.
The closest Liverpool actually came to scoring in the first half was when Steven Reid's attempted left-footed clearance of Shelvey's low cross cannoned off his standing leg and looped over the crossbar from four yards.
A lack of fluidity and crispness was noticeably absent in Liverpool's passing game as the Baggies harried and hassled and tried to stifle as much of their opponents' movement as possible.
Every pass from the hosts seemed half-a-yard too short or long and their control of the ball wasteful.
Improvements were made by Brendan Rodgers for the second half as Downing had a shot blocked and Gerrard's follow-up was crowded out before Henderson's cheeky close-range backheel from Glen Johnson's pass was stopped by Foster.
With an hour gone more work was required and Raheem Sterling and Borini were sent on for the ineffective Shelvey and the tiring Henderson.
Borini was denied by a fully-stretched West Brom goalkeeper after lashing Downing's lay-off goalwards, McAuley slid in to block Suarez's shot and the wrong-footed Foster stuck out a hand to stop Gerrard's drive.
But having dominated proceedings Liverpool were hit with the sucker punch nine minutes from time.
Chris Brunt swung over a right-wing corner and McAuley had a free run in the area to power home a header.
Liverpool went chasing the game and were exposed even later on when Lukaku, having originally been dropped to the bench, stroked home their second.
Having picked up just one point from a possible 18 the victory was vital in halting the Baggies' slide down the table.
It also extended Liverpool's unwanted record of still not having beaten a team in the top half of the Premier League this season as they saw West Brom leapfrog them into eighth.