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All four goals came in the opening 27 minutes as Chelsea's miserable run stretched to one Premier League win in seven games.
David Brooks gave the Cherries the perfect start but Bournemouth quickly showed why they have conceded more goals on the road than any other side in the English top flight.
Palmer equalised from the penalty spot before Enzo Fernandez was afforded acres of space to fire into the top corner.
But Chelsea failed to deal with a long throw for the second time when Justin Kluivert turned in Antoine Semenyo's delivery at the back post.
The home fans made clear their frustration at Maresca's decision to replace Palmer with Joao Pedro just after the hour mark.
And it could have gone from bad to worse for the Blues in stoppage time had Enes Unal not wasted a glorious chance to secure Bournemouth's first win since October 26.