Ayr United lost top spot in the Championship as Partick Thistle hit back to earn a share of the points at Somerset Park.
After his initial effort was saved, Anton Dowds converted a retaken penalty on 23 minutes following a hand ball from Aaron Muirhead.
The visitors levelled on 74 minutes when Harry Milne headed home from a Kyle Turner cross.
Ayr remain unbeaten after six league outings but slip one point behind Falkirk, who have won all five of their matches.
Thistle are fifth, with just one victory from their opening five games.
