Clarkson volleyed the hosts ahead from the right-hand corner of the penalty area after 19 minutes after Matt Harrold had controlled a Michael Smith free-kick.
Parkes doubled the advantage 12 minutes later, heading powerfully home from eight yards out after Dons goalkeeper Ross Worner had hesitated over coming out to intercept a Lee Brown corner.
Visiting midfielder Sammy Moore was sent off for a second yellow card eight minutes from time before Harrold completed a convincing win by hammering home an 89th-minute penalty after substitute Ellis Harrison had been fouled.
AFC Wimbledon twice went close at the end of the first half - centre-back Alan Bennett sent a glancing header inches wide and Andy Frampton stabbed a Callum Kennedy corner just past a post.
But Rovers threatened more goals before the break with Worner saving well from Eliot Richards.