Second half strikes from Gareth McAuley and substitute Romelu Lukaku sealed the three points and - following their 3-0 win at the Hawthorns on the opening day of the season - a first double over Reds since the 1966-67 season.
Foster saved a spot kick from Steven Gerrard when the scores were level, after Jonas Olsson was adjudged to have fouled Luis Suarez. The miss proved to be crucial as the Baggies won for the first time in eight games.
Liverpool boss Brendan Rodgers refused to be too downbeat after the defeat and praised his side's showing.
"The players gave everything," he said. "It was one of them games we couldn't get the break through.
"The longer it goes on it gives the opposition more encouragement. It was one of them games when we needed that first goal.
"We were on the front foot but it's a good away performance from West Brom. You come here, defend and as long as you can keep the score 0-0 you have always got that chance.
"I'm disappointed for the players. We have been on a terrific run especially at home, we have defended well throughout the season here."
Rodgers did not attend his post-match press conference, restricting his opinions to his contracted obligations with broadcasters.