The only goal came from Jamie Vardy, the English international raced onto Shinji Okazaki’s pass before finishing past Ben Foster in the 43rd minute.
The result sees Leicester reach virtual safety on 40 points, and the Baggies stay 8th.
First half devoid of action until late on
After a timid opening exchange, Wilfried Ndidi had the first chance of the game, his shot from 20 yards was deflected wide of Foster’s goal.
The home side dominated possession in the opening 20 minutes, in a game that quickly turned so scrappy and physical it could have been on the undercard for the Anthony Joshua vs Wladimir Klitschko fight tonight.
The first real chance of the game fell to Chris Brunt, latching onto Jonny Evans’ deep cross at the far post but his header was tipped over the bar acrobatically by Kasper Schmeichel.
Nacer Chadli then had a chance after West Brom won the ball back in Leicester half, but his low drive was straight at Schmeichel.
It was clear that this was a game between two sides who tend to employ a counter-attacking approach as neither side really wanted to commit men forward and take the game by the scruff of the neck.
Brunt then had enough time in the box to bring the ball down, once he did his half-volley was well blocked by Robert Huth.
Ndidi then had a clear chance after the ball dropped to him in the penalty area, he stabbed his left-footed effort wide though.
Vardy broke the deadlock moments later, after Okazaki intercepted a pass inside the West Brom half, moved the ball onto Vardy who finished in style.
Jamie Vardy has now scored eight goals in 12 competitive games for Leicester under Craig Shakespeare, one more than he managed in 32 appearances under Claudio Ranieri this season.
Salomon Rondon almost levelled the score right before the half-time whistle, his glancing header from James Morrison’s corner went just wide of the post.
Second half much better than the first
Leicester came out racing in the second half, Vardy was in space inside the area, his low cross was aimed towards a diving Okazaki but he couldn’t reach the cross.
The Baggies fired back moments later, as Rondon was able to bring the ball down and volley at goal from 20 yards but his effort was well saved by Schmeichel.
The second half was a polar opposite to the first. Full of life, energy and chances. Both sides appeared to have been given a talking to at half-time.
Craig Dawson almost levelled the scoreline with a header from a corner, but his goal-bound effort deflected over the bar from his own teammate.
Riyad Mahrez rippled the outside of the net, cutting inside from Drinkwater’s pass, as both sides pushed on to score the next goal.
Chadli came within inches of equalising off a free-kick, his right-footed effort fell just over the bar.
The Baggies kept piling on pressure searching for an equaliser, as sub James McClean darted past Yohan Benalouane before seeing his shot parried away.
Morrison had a free header from six yards out but his effort was straight at Schmeichel.
Mahrez came close again, cutting inside and taking his trademark bending shot to the far post but it didn’t bend enough this time and Foster looked relieved to see it go wide.
Rondon saw another glancing header go wide as the sides approached the final five minutes of the game, with West Brom pushing to equalise.
Leicester saw the game off well. Didn’t give away any real chances and held the ball up when they were in possession during the dying embers of the game.
All in all, Shakespeare will be the happier of the two managers after seeing his side claim all three points in a tight game, and reaching 40 points, which didn’t look so easy when he first became head coach.