Morton started briskly, testing Ludovic Roy in the Ayr goal first with a Chris Templeman low shot and then with a James McAlistair downward header from a Chris Millar cross.
In the 11th minute Templeman's pass gave Millar a chance to run directly at the Ayr goal, and he duly converted a crisp, low shot.
A minute later Morton were back testing the Ayr rearguard, and this time John Maisano fired a swirling left-foot drive past Roy.
Ayr's Gareth Wardlaw had earlier blazed over a reasonable chance, but the main threat to Morton came from debutant Stuart Boyd, and Stewart Greacen had to make a brave block to prevent the striker opening his account.
Andy McLaren almost scored from a Templeman cross and Roy fisted away a powerful rising drive from Millar. The Ton ended the half with a thrilling move. Peter Weatherson released Andy McLaren down the right wing, and the experience forward's cross was not cleared and Weatherson himself came close with a powerful drive from 20 yards which just cleared the bar.
Boyd lifted Ayr on the restart with a bold run at David McGurn's goal but blazed over.
Mark Smyth lifted them even more with a low shot from 35 yards which McGurn seemed slow to see and the ball went through his hands and into the corner of the net.
Weatherson struck a post but Ton couldn't score a third and almost ended up dropping two points in stoppage time when Boyd went clean through but pushed his shot wide.