Youssouf Mulumbu, James Morrison and Paul Scharner scored second-half goals for West Brom, which claimed a first league win since January 15 to climb into 16th place and above Birmingham.
Host Birmingham came back down to earth after beating Arsenal 2-1 to win the League Cup last Sunday, falling apart after Chile midfielder Jean Beausejour had made it 1-1 in the 48th minute.
It was West Brom's first victory since former Liverpool manager Roy Hodgson took charge of the team on February 10, and a vital one considering how tight the table is at the bottom.
"We knew Birmingham were around us (in the table) and the lads stood up and did a good job today," said Morrison, who scored the standout goal of the match.
Birmingham shaded a poor first half but conceded two minutes into the second when substitute Peter Odemwingie stabbed the ball through to Mulumbu, who poked a rising shot past goalkeeper Ben Foster from 12 yards.
The home side replied barely 60 seconds later through Beausejour, who slotted home at the far post after meeting a low cross from Lee Bowyer.
West Brom, though, started to dominate possession and retook the lead when Morrison collected a pass from Steven Reid, spun past a leaden-footed Curtis Davies and smashed a left-footed shot home from 18 yards.
West Brom midfielder Chris Brunt slammed a shot against the post before Scharner made the game safe in the 72nd, latching onto Morrison's cross and powering in a header that Foster couldn't prevent from crossing the line.
"I thought the players worked really hard," said Hodgson, whose team had previously drawn three straight games since he joined. "Perhaps we were lucky to catch Birmingham on a bad day, but we ran out worthy winners.
"They had their cup final last Sunday. This was a cup final for us."