The advantage lasted just 13 minutes as Jamie Vardy put Leicester back on level terms with an even better volley, latching on to a superb long pass from Mahrez to fire home his 14th Premier League goal of the season.
Mahrez then latched on to substitute Kelechi Iheanacho's pass to dink the ball home and give Leicester the lead just after the hour mark.
Iheanacho's 76th-minute header made it 3-1, prompting many of the home fans to head towards the exits.
Vicente Iborra's stoppage-time header rounded off another dismal day for struggling West Brom.
West Brom stayed rooted to the bottom, eight points from safety, while Leicester are eighth on 40 points.
(Reporting by Philip O'Connor, editing by Pritha Sarkar)
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