Chelsea could only draw 2-2 at home to Bolton on Saturday, which allowed Manchester United to increase their Premiership lead to five points.
United won 4-2 at Everton in the other early kick-off and with three games left, the Red Devils look set to take the league title.
Jose Mourinho made six changes for the Trotters match, with Frank Lampard and Didier Drogba among the players rested.
Lubomir Michalik gave the visitors a shock 19th-minute lead from close range, but three minutes later the Blues were level through Salomon Kalou's glancing header.
Ricardo Carvalho limped off injured, and then Jussi Jaaskelainen put through his own net 34 minutes to give the reigning top-flight champions the lead.
But Kevin Davies headed home Idan Tal's 54th-minute free-kick to equalise and despite substitutes Lampard, Drogba and Joe Cole all going close, Sam Allardyce's battlers held on.