Petersfield lost opener Jake Hastie early on for a duck, and Henry Shore then followed for 25.
Dave Marshall (54), Tom Sherry (16), Hans Mai (41) and Mark Butcher (33 not out) all made good contributions as Petersfield finished on 192-7 at the end of their allotted 45 overs.
Tim Loescher (2-15), Danny Grimson (1-24), Matt Birch (1-36) and Craig Collins (3-25) were the Michelmersh and Timsbury wicket takers.
The hosts lost Adrian Parsons early on in their reply when he was run out for six, but Matt Perriam (26), Steve Turner (11), Tom Holland (57), Collins (13) and Josh Moore (24) all made useful contributions to keep the home side on course for victory.
Petersfield took wickets at regular intervals, but Loescher (21 not out) held his nerve to see the hosts home to victory in the 40th over.
Harvey Baker (1-47), Richard Stephens (3-27), Shore (2-35) and Nathan Barlow (1-30) were the Petersfield wicket takers.