On a day when Spurs fought back to earn a 2-2 home draw with Bournemouth, Marc Cucurella struck a 60th minute winner for Chelsea at Stamford Bridge on Sunday after Cole Palmer's first-half penalty was saved.
Victory boosted Chelsea's chances of a return to the Champions League next season, moving them ahead of four-time defending champions Manchester City, who'd lost 1-0 to Nottingham Forest a day earlier.
Enzo Maresca's team took full advantage of City's latest loss as Cucurella's long-range effort was drilled low into the corner to beat Leicester goalkeeper Mads Hermansen.
Earlier, Hermansen had been the visitors' hero when diving low to save Palmer's penalty in the 22nd.
It was the first time Palmer had failed to score from the spot in the league in 13 attempts, his 100 per cent record from his previous 12 having been a league record.
The 2016 champions Leicester are now six points adrift of safety in the relegation zone.
At Tottenham Hotspur Stadium, Son Heung-min's late penalty completed an unlikely comeback for Ange Postecoglou's men after Champions League-chasing Bournemouth had dominated the chances.
Marcus Tavernier gave the visitors the lead in the 42nd minute and Evanilson doubled the advantage in the 65th, while Justin Kluivert also hit the post.
Pape Sarr's mis-hit cross then caught out Bournemouth goalkeeper Kepa Arrizabalaga and flew into the back of the net in the 67th minute to give Spurs hope.
And it was Arrizabalaga's error - bringing down Son in the box - that led to the equaliser from the penalty spot as Son stepped up to convert.
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