A controversial penalty scored by Cesc Fabregas denied West Ham a first win at Chelsea in 14 years.
Fabregas converted an 89th-minute spot-kick to earn a 2-2 draw after referee Bobby Madley adjudged Ruben Loftus-Cheek had been tripped by Michail Antonio. Replays suggested if there was contact it was minimal and outside the area.
Andy Carroll thought he had enhanced the Hammers' bid for Champions League qualification when he scored one minute after coming off the substitutes' bench, but Fabregas scored his second after a brilliant free-kick had earlier cancelled-out Manuel Lanzini's superb opener.
West Ham remained fifth, one point behind Manchester City and without a double over Chelsea since the 2002-03 season, while the Blues' unbeaten league run was extended to 14 games, 13 of those under interim boss Guus Hiddink.
Chelsea were aiming to recover from two cup exits in four days, the second of which saw Diego Costa dismissed. The suspended striker was replaced by Loic Remy, who made his first start since September.
Chelsea's FA Cup exit at Everton followed the loss to Paris St Germain, which might have been the Blues' last Champions League appearance for some time.
The Hammers are bidding to play Europe's elite at the Olympic Stadium next term and made a fine start against Chelsea, pressing their derby rivals into a mistake which led to the opening goal.
Gary Cahill was caught in no-man's land when Diafra Sakho headed the ball on, John Obi Mikel slid in on Dimitri Payet but danger still lurked. The ball broke for Lanzini, who picked his spot.
Payet drove a shot just wide as the visitors continued to apply pressure before Cahill pleaded for a handball against Enner Valencia. Replays showed the ball hit the West Ham forward's shoulder.
West Ham had Chelsea back-pedalling again when Sakho and Lanzini released Aaron Cresswell, forward from left back. Branislav Ivanovic made a last-ditch block.
Willian went close with a free-kick before Chelsea equalised when Fabregas curled in from 25 yards after Winston Reid had fouled Oscar.
Chelsea thought Adrian had handled the ball outside the area as the hosts poured forward at the start of the second half.
Ivanovic, at right-back as a fit-again John Terry made his first start in seven games and his 701st Chelsea appearance, rampaged down the flank. He crossed for Oscar, who opted to use his right foot. It was the wrong choice.
Pedro, on at half-time for Kenedy, next found Remy, who turned and forced Adrian to collect his shot at the second attempt.
Chelsea were caught as they pressed forwards. Carroll, on moments earlier, made an arcing run behind Ivanovic and stayed onside as Cahill and Terry appealed.
Payet found him and Carroll did the rest. He thought it was his second winner over Chelsea this season after his header at Upton Park in October.
But Chelsea continued to threaten. Substitute Bertrand Traore and Oscar had shots blocked, Fabregas headed off target from a corner and then acrobatically fired over.
Traore cleared a Carroll header off the line from a corner before Loftus-Cheek broke and went down in the box. Fabregas converted.
Payet had a free-kick saved after a squabble involving all 20 outfield players and Loftus-Cheek fired wide as neither side could find a winner.
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