Scott Chaplin headed the winning goal from six yards after a neat move in the ninth minute.
Ayr dominated the first half and could have been five up by the break.
After Chaplin had nodded home a Stuart McGrady cross he had another header cleared off the line.
Stuart Boyd blew two great chances then went close for the third time with an effort which flew just over the top.
Forfar were brighter in the second half and Ricky Waddell had a volley cleared off the line by Barry McLaughlin.
Chaplin had calls for a penalty turned down when he was fouled by Jay Stein.
It ended with tempers raised as substitute Andy Ferguson was sent off in stoppage time after tangling with Forfar defender Eddie Forrest.