Sam Allardyce's side put their bodies on the line throughout the 90 minutes to deny the Blues a much-needed three points.
Spanish keeper Adrian was unbeatable as he produced a series of fine saves - while in front of him James Collins, Matt Taylor and James Tomkins produced some heroic blocks to keep the blue shirts at bay.
The Hammers could even have pinched all three points but the returning Andy Carroll - who had a good first-half shout for a penalty turned down - squandered a great opening when he swung and missed Stewart Downing's centre.
Jose Mourinho sent on Frank Lampard, Nemanja Matic and Demba Ba in an attempt to find the crucial breakthrough but the Hammers stood firm to see Chelsea - who had 39 shots during the contest - drop behind table-topping Manchester City, who they face on Monday Night Football.
Lampard thought he'd earned the win with the last kick off the match only for Adrian to deny him with an amazing goal-line stop just moments after Samuel Eto'o had the ball in the net, with referee Neil Swarbrick ruling he had blown for an earlier foul on the keeper.
Mourinho on Tuesday played down his side's title chances this term and the Blues saw a seven-game winning run ended.
City scored nine in the two-legged Capital One Cup semi-final with the Hammers, but the Blues faced a defensive wall they could not breach while the visitors also posed an early threat.
Carroll slipped at the far post with Cesar Azpilicueta in close attendance after seven minutes and referee Swarbrick was unmoved at the Hammers' penalty appeals, much to Allardyce's frustration.
Oscar's curled effort was helped on to the bar by Adrian and Petr Cech scrambled clear a Tomkins header before the West Ham goalkeeper saved from John Terry and Eto'o late in the first half.
Willian, Eto'o and Ramires blazed over as Chelsea were limited to shots from range.
Mohamed Diame's fall over the advertising hoardings resulted in a change, with Matt Jarvis replacing the Senegal midfielder, who limped off pointing at his right knee.
Adrian twice had to be alert, saving a Terry header with his feet before turning an Eto'o shot around the post.
West Ham's threat was limited to long balls directed to Carroll, which Cahill and Terry, who caught the Hammers striker with an accidental flailing arm on one occasion, dealt with.
Chelsea showed more urgency after the break. Oscar shot straight at Adrian, there was no-one in the six-yard box to meet a Willian cross and Ramires fired wide from an Azpilicueta cross.
Joey O'Brien's challenge on Willian was an outlet for Mourinho's frustrations before Chelsea earned a reprieve when Carroll swung at thin air when Downing crossed towards him.
Substitute Lampard had scored three times in his previous two contests with his former club and had half-chances to add to the tally.
Little was coming off for Chelsea and, in another attacking substitution, Mourinho threw on another ex-Hammer in Ba for Oscar, while Antonio Nocerino came on for his West Ham debut.
O'Brien went off as the Hammers faced four minutes of stoppage time a man short and Adrian saved from Ba before Eden Hazard shot wide and had an effort saved.
Adrian placed the ball on his six-yard box after being awarded a free-kick in the follow-up to Hazard's shot, but Eto'o put the ball in having not heard the whistle.
Lampard was denied in the 97th minute by a fine Adrian save as the Hammers earned a valuable point and denied Chelsea an eighth successive win in all competitions.