Craig Conway beat two players before drilling home a low deflected shot on 26 minutes to put Robert Connor's men in charge.
A minute later Dumbarton saw red when Scott Bannerman was sent off for a bad challenge on Jerome Vareille. Ayr cashed in when Douglas Ramsey raced into the box to head home a cross from Craig Conway after great work by Gareth Wardlaw.
Dumbarton never gave up and Andy Rodgers shot high and wide while they forced a series of corners which came to nothing.
Chris Strain and Raymond Logan had goalbound shots superbly tipped over by keeper Stephen Grindlay as Ayr pressed in vain for a third.
Ayr boss Robert Connor said: "Getting three points was a big thing but was I disappointed that we did not capatilise in the second half when the final delivery wasn't good enough."
Dumbarton boss Paul Martin said: "One thing that is concerning me is our inability to make our chances count in front of goal."