Brendan Rodgers's team had scored 12 times in their last three Premier League home games to renew their ambitious long-term plans of returning to the top four but they were shell-shocked by Gareth McAuley and Romelu Lukaku's late goals.
Chances and possession were wasted and Liverpool's night had been summed up with less than 15 minutes remaining when captain Steven Gerrard saw a spot-kick, which was contentiously won by Luis Suarez, saved by heroic West Brom keeper Foster.
For West Brom, who before kick-off had kept just one clean sheet in their last 29 Premier League away games - with that shutout coming at Anfield in their 1-0 win in April 2012 - it was a first win in eight in all competitions but attention will focus on Liverpool's misery.
In what was a scrappy beginning, Jonjo Shelvey, starting in place of Liverpool's injured £12m striker Daniel Sturridge, had an early finish correctly disallowed for offside after Foster had spilled Glen Johnson's dipping shot.
And, despite not taking the lead, the chalked-off effort at least gave Liverpool some spark, with the rejuvenated Stewart Downing proving a menace down the right and Luis Suarez producing a wonderful, backheeled, flicked cross on the left.
West Brom, who had January transfer deadline day rebel Peter Odemwingie in their travelling party but not in the matchday squad, offered little as an attacking threat but they would have been relatively happy.
However, Baggies boss Steve Clarke, a former Liverpool coach, would have known his visitors were fortunate not to concede before half-time as Steven Reid almost netted an own goal when scooping over the crossbar.
Jordan Henderson took a leaf out of Suarez's book at the start of the second half, producing his own backheel in an attempt to open the scoring from a low Johnson cross from the right in front of The Kop.
With 35 minutes remaining, West Brom - who humbled Liverpool 3-0 at The Hawthorns on the opening day of the season - were becoming a little more adventurous and that led to a more open, end-to-end game.
Rodgers decided to send on Fabio Borini and Raheem Sterling in place of Shelvey and Henderson but West Brom were continuing to make life difficult for their hosts, with a Gerrard shot well saved by Foster.
And, in the 76th minute, Foster was again to deny Gerrard when, after Suarez had gone down a little softly in claiming a push from Jonas Olsson, the West Brom goalkeeper dived low to his left to save the midfielder's penalty.
It proved an incredibly costly failure from Gerrard as, in the 81st minute, West Brom scored with just their second shot of the match when McAuley headed home from a corner.
And, in the final seconds before injury time, West Brom added to Liverpool's woe with a breakaway which resulted in substitute Lukaku putting the result beyond doubt and moving his club above their hosts to eighth in the table.