Josh King scored twice while David Brooks and Charlie Daniels were also on target as Chelsea’s recent struggles in the Premier League continued.
However, the visitors started the match well and almost took the lead in the seventh minute when Cherries goalkeeper Artur Boruc managed to tip Mateo Kovacic’s onto the crossbar.
Boruc then saved Eden Hazard’s dipping shot as Chelsea dominated the opening stages.
Bournemouth grew in confidence as the first period wore on though and Brooks saw his 25-yard effort saved by Kepa Arrizabalaga in the Chelsea goal.
Howe’s side made the perfect start to the second half when the impressive Brooks played in King whose first-time shot was too good for Kepa.
Bournemouth doubled their lead midway through the second period when King set up Brooks who beat David Luiz before slipping the ball home.
Chelsea had no answers and incredibly Bournemouth added a third goal with 15 minutes remaining when Nathaniel Clyne sent Junior Stanislas clear and his cross was turned home by the unmarked King.
Maurizio Sarri’s team conceded another goal in stoppage time when Daniels got on the end of Jordon Ibe’s free-kick and on this form the Blues face a real struggle to secure a place in next season’s Champions League.