May's second effort from 25 yards was spilled by Morton keeper Nicolas Caraux and McDonald pounced to bundle the ball over the line to send the visiting fans into raptures and the home supporters into rage.
There was some chaos after the final whistle with Ton manager Allan Moore raging at the officials.
The Greenock side went into the game bottom of the Championship and without a win since causing the surprise of the competition by knocking out Celtic in the last round and will feel aggrieved.
Perth midfielder David Wotherspoon hit the post with a free-kick with 16 minutes remaining but there was little between the teams for most of the game until McDonald sent the Perth men into Thursday's draw.
- Sports & Recreation
- Nacho Novo