We forged ahead in an even first half through goals from Harry Kane and Heung-Min Son but the Blues hit back through Gary Cahill and substitute Eden Hazard after the break.
Several players found their way into referee Mark Clattenburg’s notebook in an ill-tempered affair but ultimately it was the result that mattered and it was one that left us seven points adrift of the Foxes with only six more to play for. Claudio Ranieri’s men, who could have secured the title with victory at Manchester United on Sunday, were therefore assured of top spot.
The last time we defeated Chelsea on their own patch, meanwhile, was back in 1990.
Mauricio Pochettino was forced into one change at the beginning of the night as Son was handed a start in place of the suspended Dele Alli while Eric Dier recovered from a concussion against West Bromwich Albion to anchor the midfield alongside Mousa Dembele. Meanwhile, Clinton Njie returned to the bench having been missing since December with a knee injury.
The home side too had an injury boost as John Terry returned after a spell on the sidelines with an Achilles problem.
There was an electric atmosphere inside Stamford Bridge and it was a frantic start with several early challenges flying in. Cahill had the first chance of the game inside five minutes but headed wide from a corner.
Our first opportunity came in the 11th minute when Danny Rose fizzed a dangerous shot narrowly over from distance. It sparked the best spell of pressure in the opening exchanges as we settled down after the highly-charged start.
It was only at the midway point of the half that the tempo started to ease. The end-to-end pattern of fast counters gave way to a more patient and sustained build-up from both teams with us shading the possession and territory. The home side had the best chance, though, when Diego Costa fed Cesc Fabregas, who rolled a measured effort wide.
We responded well when Erik Lamela found Son on the edge of the Chelsea box but he bent his shot the wrong side of the post.
Kane tried his luck with a free-kick from 40 yards but both goalkeepers remained untested as we ticked past the half-hour mark.
That soon changed when Costa pounced on a stray pass from Kyle Walker and forced Hugo Lloris into a fingertip save from distance.
With 10 minutes of the half remaining we grabbed the lead. Lamela showed perfect vision and execution to slip in Kane who shimmied past Asmir Begovic and slotted into the empty net. It almost got better soon afterwards when Walker slipped the ball back for Lamela, whose shot was blocked by Cahill inside the area.
Son doubled our lead just before the interval. Branislav Ivanovic gave the ball away to Kane who found Eriksen beside him. The Dane kept his composure to spot the run of Son, who galloped through the Chelsea defence and slotted past Begovic.
The game had simmered at boiling point for much of the half and bubbled over just before the interval when a Rose challenge on Willian sparked a large coming together in front of the dugouts.
Kane had two early chances in the second half but Begovic saved comfortably on both occasions. Son then rolled another effort just wide after Rose and Kane had led the charge.
The challenges continued to fly in with Lamela becoming our fourth player booked for a late challenge on Fabregas.
Chelsea found a way back into the game just before the hour mark when Cahill seized upon a loose ball from a corner and lashed home from 12 yards.
The introduction of Eden Hazard at the break had given the home side more drive and they cranked up the pressure after the goal. We looked like we had weathered the storm with 20 minutes to go, however, as we wrestled back some momentum and restored some calmness to our play.
Substitute Ryan Mason almost sealed it with 15 minutes to go when he forced a low save from Begovic from a decent opening. Eriksen saw his angled shot from the rebound blocked.
Rose was forced off moments later, replaced at left-back by Ben Davies, but our defence was undone on 83 minutes as Costa played in Hazard and he curled into the top corner from just inside the box.
The game remained hotly-contested although chances for the remainder of the match were at a premium. Fabregas saw a free-kick easily repelled by our defence but there was a further blow in stoppage time as Toby Alderweireld was forced off. Dier dropped into the back four with Nacer Chadli on in his place, but the game drifted to a conclusion amid another flurry of yellow cards and we were left to reflect on what might have been.
Chelsea (4-2-3-1): Begovic; Ivanovic, Cahill, Terry (c), Azpilicueta; Mikel, Matic (Oscar 77); Willian, Fabregas, Pedro (Hazard 46); Costa. Substitutes (not used): Amelia, Baba, Loftus-Cheek, Kenedy, Traore.
Spurs (4-2-3-1): Lloris (c); Walker, Alderweireld (Chadli 90+1), Vertonghen, Rose (Davies 82); Dembele, Dier; Son (Mason 64), Eriksen, Lamela; Kane. Substitutes (not used): Vorm, Wimmer, Carroll, Clinton.
Goals: Chelsea – Cahill 58, Hazard 83. Spurs – Kane 35, Son 44.
Yellow cards: Chelsea – Willian 45, Ivanovic 71, Mikel 87. Spurs – Walker 27, Vertonghen 38, Rose 45, Lamela 51, Eriksen 70, Dier 87, Kane 90+5, Dembele 90+5, Mason 90+6.
Referee: Mark Clattenburg.