A first-half goal from Wilfred Ndidi and Jamie Vardy's 15th league goal of the season proved enough to secure a priceless victory for Enzo Maresca's side.
Jed Wallace halved the deficit for West Brom in a game where they created the best opportunities, Hamza Choudhury incredibly making three goalline clearances, but they were unable to earn the share of the spoils that they deserved.
The East Midlands outfit now sit two points clear of second-placed Ipswich Town and, more importantly, four points ahead of third-placed Leeds United with three matches remaining.
Meanwhile, West Brom remain in fifth spot in the standings with just two matches left, Carlos Corberan's side hoping that results go their away in order to feel more secure of a top-six place.
Leicester establishe lead against run of play
Leicester went into this contest considerably low on confidence given their recent form, and that almost contributed to an opening goal being conceded within three minutes, Okay Yokuslu blazing wastefully off target after a mix-up between goalkeeper Mads Hermansen and Choudhury.
Before the quarter-hour mark, Choudhury had to get back to clear a Mikey Johnston effort off the line, before the Baggies winger forced a save out of Hermansen with a low drive.
While the Foxes had been second best, they were ahead in the 22nd minute. After West Brom goalkeeper Alex Palmer had saved a Vardy header, Ndidi reacted quickest to slot home the rebound.
Although West Brom continued to look the more threatening, Leicester could have doubled their lead before half time. Yokuslu brought down Vardy just inside the penalty area, only for the veteran forward to smash his spot kick off the crossbar.
West Brom fail to equalise in remarkable passage of play
Despite Leicester starting the second half on top, West Brom somehow did not equalise in the opening six minutes after the restart, Choudhury pulling off two more goalline clearances.
Having initially slid behind Hermansen to prevent Diangana's low shot from finding the bottom corner, Choudhury got back to his feet to head the ball over the bar after the rebound nearly ricocheted off Diangana's hand and into the net.
From the resulting corner, Cedric Kipre sent a header against the crossbar, with Diangana unable to rearrange his feet at the back post to convert from three yards.
Moments later, Vardy was the next to fail to score from inside the six-yard box, miskicking at the back post, before back down the other end, Diangana directed a first-time strike wide from eight yards out, much to his frustration.
West Brom were ultimately made to pay midway through the second half. A cross from Abdul Fatawu was perfect for the awaiting Vardy in the middle of the penalty area, and the former England international did the rest with a header from six yards.
There were signs that the game could peter out, Leicester content to try to see the game out, but West Brom found a lifeline with 14 minutes left, Kipre picking out the run of Wallace with a sublime through ball and the forward did the rest with a cool finish into the bottom corner.
While West Brom continued to pose a threat, Corberan's side failed to create any notable chances during the closing stages, but credit should go to Leicester for ending a two-game losing streak with a hard-fought win, perhaps the most important of their season to date.