Jose Mourinho's side produced another disjointed display and were stunned in the 82nd minute when substitute Glenn Murray, who had only been on the field for two minutes, headed home after a goalmouth scramble.
Chelsea's eighth defeat in 15 Premier League matches since the start of the season left them in 14th place, 14 points behind fourth-placed Manchester United.
Bournemouth moved out of the bottom three.
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"The guys did great before I came on and sort of controlled the game at times," Murray told Sky Sports.
"When it's 0-0 after 80 minutes they were more nervous than us because we don't expect anything out of these games really."
Chelsea had been unbeaten in their past 43 home league games against newly-promoted teams, winning 37.
But Bournemouth, enjoying their first taste of top-flight football after a rapid rise from obscurity, were always in with a chance as Chelsea pushed hard for a winner.
Mourinho again left Diego Costa on the bench, but even when the Spain striker did come on for the second half, replacing Oscar, the Blues could not find a way through and failed to score at home in the league for the first time since May 2014.
(Reporting by Martyn Herman; editing by Toby Davis/Alan Baldwin)
