Tottenham, needing to win to take the title race to the penultimate weekend of the season, were deservedly ahead at halftime through goals by Harry Kane and Son Heung-min.
But Gary Cahill halved the deficit just before the hour mark and second-half substitute Eden Hazard's 83rd-minute curler handed the title to Leicester.
With two games left Leicester are seven points clear and Tottenham need three points to secure runners-up spot.
A bad-tempered game produced a rash of yellow cards and several players were lucky to stay on the pitch while tempers boiled over at fulltime.
Tottenham had already gone close with Danny Rose's pile-driver and Son curling wide before they opened up Chelsea's defence again.
Erik Lamela's clever pass found Kane just onside and the England striker kept his cool to round Asmir Begovic and slot home his 25th league goal of the season.
Tottenham doubled their lead just before halftime when Chelsea squandered possession and Christian Eriksen played in Son who guided a shot past Begovic.
Rose and Willian squared up before the interval and Tottenham manager Mauricio Pochettino found himself on the pitch trying to separate the players.
Chelsea sent on Hazard after the break and the Belgian playmaker gave the home side a greater threat.
Cahill stabbed home through a crowd of players to give Chelsea hope after 58 minutes Spurs were rocking.
The visitors recovered their poise, though, and substitute Ryan Mason went close to making it 3-1 before Hazard picked out the top corner with an unstoppable effort.
(Reporting by Martyn Herman, editing by Ed Osmond)
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