Clarke's goals were the first by a Crawley striker for 10 games and MK Dons, despite some good approach play, went down to defeat after hitting the crossbar twice in the first half.
Crawley scored with their first serious threat on goal after 21 minutes when a corner from Nicky Adams was flicked on by Gary Alexander for former Blackpool forward Clarke, who fired in an angled shot into the top corner.
Clarke sealed victory a minute from time by expertly turning in a cross from substitute Mark Connolly.
Dons keeper David Martin denied Josh Simpson shortly after Clarke's opener by turning his rasping goal-bound drive away for a corner.
Crawley keeper Paul Jones got the better of former Reds striker Charlie MacDonald in a one-on-one situation, but was beaten when a shot from Daniel Powell struck the underside of the bar and was cleared. The hosts had another let-off just before the break as MacDonald's right-foot shot struck the crossbar.