May struck his first goal six minutes before the break to gives Accies a deserved lead.
The Accies striker had a couple of chances before that, sending a lob into the hands of David Hutton and then slipping another effort wide.
Hamilton almost came close to increasing the advantage shortly after the break when Martin Canning sent a header against bar.
At the other end Morton midfielder Martin Hardie tested Kevin Cuthbert with a free-kick, which the Accies keeper did well to save.
May scored his 25th goal of the season to settle the match when he turned the ball in at the back post from an Ali Crawford cross.