Jamie Vardy struck the decisive goal for Nigel Pearson's side in stoppage time as Leicester recorded back-to-back wins to move just three points behind fourth-bottom Hull City with a game in hand.
Darren Fletcher had given Albion the lead inside the opening 10 minutes with his first goal for the club, only for David Nugent to bring Leicester level with his fifth goal of the campaign.
Craig Gardner's perfectly executed volley gave Tony Pulis' side the lead once again before the break, but Leicester posed more of an attacking threat in the second half and were rewarded in a dramatic finale.
A Robert Huth header restored parity with 10 minutes to play, before Vardy sealed a huge win in their fight against relegation.
It was a second successive home defeat for Albion, who are seven points above the drop zone.
Wearing a commemorative 1968 kit in honour of former striker Jeff Astle, West Brom made a vibrant start and fired an early warning as Joleon Lescott headed over after six minutes.
Leicester – who made one change from their victory over West Ham – failed to heed that caution as the home side took the lead two minutes later.
Fletcher rose unmarked at the front post to flick in Chris Brunt's corner, with goalline technology awarding the goal despite Esteban Cambiasso's attempts to clear.
Leicester restored parity after 20 minutes as Leonardo Ulloa beat Gareth McAuley in the air from a quick free-kick, his knock-down perfect for Nugent to poke the ball under Boaz Myhill.
They were not level for long, though, as Wes Morgan failed to clear Brunt's teasing cross and Gardner lashed in from 12 yards – much to the frustration of Leicester, who felt the ball had gone out for a throw in the build-up.
Ulloa should have sent the sides in level at half-time as Leicester's strike partnership combined again after 42 minutes, but he blazed over from eight yards.
Pearson will have been pleased with Leicester's promising start to the second half, but the visitors lacked quality in front of goal and they struggled to stretch Myhill.
Victor Anichebe's introduction on the hour-mark gave Albion more attacking threat, while fellow substitute Jonas Olsson could have also extended their lead further with two headed chances in the space of a minute.
With time running out Leicester finally got the goal their pressure deserved, Nugent clipping a cross back into the six-yard box where Marcin Wasilewski and Huth combined to bring the sides level again.
And Leicester were not finished yet, as Vardy teased the Albion defence before slotting home a low shot to secure a precious win.
