The visitors then hung on easily in a second half spoilt by a rash of yellow cards and a succession of substitutions.
Stranraer were full of fire in the opening stages could well have struck two goals with Gary McPhee and skipper Allan Jenkins being denied by Ayr keeper Ludovic Roy.
But the visitors weathered the early storm and must have thought it was Christmas all over again when home keeper Martin McCaulay dropped a cross from Michael Dunlop in the 27th minute. The ball landed right at the feet of Craig Conway who only had to slot it home from all of three yards.
With three minutes of the half left the home keeper slipped again, failing to cut out a cross ball following a brilliant run by Stuart McGrady and this time it was Gareth Wardlaw who was on the spot to score easily.
Then came what can only be described as a bizarre second half with Ayr being clever enough to deny Stranraer possession and hold on fairly easily to their two-goal lead.
Just after the hour McCaulay showed he was a good keeper with a very brave save at the feet of Paddy Connolly but in the 66th minute he was yellow carded for bringing down Wardlaw just outside the box.
The yellow fever then spread rapidly with five more bookings handed out in quick succession.
It was almost an anti-climax when, after a bit of football, a Jenkins drive hit the foot of the bar. It was Stranraer's second strike against the woodwork - near but not near enough.