Two late goals finally gave Frank Lampard his first win since his return as Chelsea’s interim manager in April.
The Blues had lost all four Premier League games since Lampard’s return in April, but had led through Conor Gallagher’s early header.
Matias Vina levelled for Bournemouth, but Benoit Badiashile and Joao Felix struck inside the last 10 minutes.
Relegation remains a possibility for the Cherries with three games left, while Chelsea are 11th in the table.
With Pierre-Emerick Aubameyang and Raheem Sterling among five players left out from the side that had lost 3-1 at Arsenal in their previous outing, Chelsea were much improved with 21-year-old Noni Madueke a particular threat on the right-hand side.
Bournemouth’s best spell came early in the second half when Vina missed a chance for a second and Dango Ouattara headed over from close range, but Gary O’Neil’s side still have a good chance of avoiding a quick return to the Championship with games against Crystal Palace, Manchester United and Everton to come.
They are currently nine points clear of the bottom three, although some teams still have four matches to play.
