Newly-promoted Chesterfield broke their League One duck with the victory, while Bournemouth crashed to a fifth successive defeat.
Chesterfield had gleaned only two points out of their initial six matches since lifting the League Two championship last season, but once Mendy had headed them into a 32nd-minute lead at Dean Court there was no looking back.
Mendy’s first goal in English soccer – he has been playing in the Czech Republic for the past eight seasons – came completely against the run of play, Bournemouth having forced a spate of corners before the Frenchman scored from Clarke’s byline cross.
Chesterfield doubled their lead on the hour – Westcarr cutting in from the left to send a rasping left-foot shot into the top corner.
The profligate Marc Pugh saw a shot palmed onto the Chesterfield crossbar before the on-loan Clarke celebrated his Spireites’ debut with a third midway through the second half.
Playing his first match since his much publicised tunnel punch-up with Swindon boss Paolo Di Canio a fortnight ago, Clarke scored from close range – only to be booked for over-celebrating.