The west Londoners came back from trailing to a Craig Bellamy strike to stay in second place just one point behind Liverpool, who also failed to win this weekend.
Chelsea's home form is alarming as they have now dropped 14 points at Stamford Bridge.
West Ham were fully deserving of their share of the spoils for refusing to hold back and they frequently disturbed the home defence.
Chelsea bossed the opening stages of the match and a Frank Lampard rasper from 30 yards was deflected for a corner by Calum Davenport on 20 minutes.
But it was the visitors who drew first blood with their first real attack on 33 minutes.
Mark Noble battled down to the Chelsea byline before cutting the ball back to Craig Bellamy ten yards out.
The Wales striker took a touch before lashing home with his right foot between Petr Cech and the goalkeeper's right-hand post.
Chelsea boss Luiz Felipe Scolari replaced Michael Ballack at half-time with Didier Drogba and the plan worked as within six minutes the Blues were level.
A moved started in midfield by Lampard saw the ball fizz first to John Obi Mikel and then to Drogba.
Lampard then dinked the ball into the path of Anelka who tucked home a smart right-footer past Robert Green from eight yards to notch up his 14th of the season and 100th career goal in the Premier League.
Lampard let fly from just outside the penalty area on 56 minutes but Green collected the ball with a smart save and the same player forced an even better stop from the keeper moments later.
Chelsea almost went into the lead when, from a corner, Drogba smashed a fierce drive but Green produced an excellent save to parry the ball away.
Salomon Kalou replaced Joe Cole on 74 minutes and the winger immediately had a strike on goal which was again saved by Green.
Green almost gifted Chelsea a goal after spilling a Lampard corner onto his own crossbar on 79 minutes before saving well from Drogba seconds later.
Chelsea appealed for a penalty two minutes from time when Lampard appeared to be upended by Lucas Neill, but referee Mike Riley waved play on.
Cech saved brilliantly from Carlton Cole who found himself with just the goalkeeper to beat in the last minute but could not find a winner for the hard-working Hammers.