Chelsea handed a Premier League debut to new signing Gonzalo Higuain on the south coast.
The Blues could have moved three points clear of Arsenal in the race for a Champions League spot but were well below par.
King opened the scoring in the first half before David Brooks added a second just after the hour mark.
Chelsea dominated possession but couldn't find a breakthrough and the excellent King soon added his second.
There was still time for Charlie Daniels to get in on the act in added time.
Bournemouth were fortunate to be level at the interval as Artur Boruc produced five impressive saves to deny a Chelsea side that failed to penetrate their hosts' defence despite 70% of possession.
But the hosts took just two minutes of the second half to go in front as King arrived late in the Chelsea box to smash Brooks' cutback past goalkeeper Kepa Arrizabalaga.
The duo combined again for the second as King lofted the ball over a scrambling Chelsea defence for Brooks to latch on to and fire into the bottom corner.
The influential Welshman hobbled off in the second half, but King added a third with the final touch of a flowing Bournemouth move - a right-footed finish from close range.
Substitute Daniels produced the finishing touch within a minute of being on the pitch with a stooping header in injury time.
A second consecutive league win for Bournemouth moved them up to 10th in the table, while Chelsea drop to fifth by virtue of scoring fewer goals than Arsenal.