The deserved equaliser came in the 24th minute from a free kick conceded on the right of the penalty box. The ball entered the area and was poorly defended and a miss-hit clearance fell nicely for Liam Buchanan to rifle home past Allan Creer.
Alloa handed Cowdenbeath another shock on the stroke of half-time when David McClune picked up a loose ball on half-way. As he moved towards goal the Fifers defence backed off until he was within range to hammer a well-directed shot past the surprised Orr.
Alloa made the better start after the interval and the Cowdenbeath defence were subjected to 15 minutes of sustained pressure during which Alloa's Graeme Brown struck the bar from point-blank range.
The visitors did have chances and Creer earned his bonus by turning away another net-bound effort from Buchanan at the expense of a corner.
Alloa's Stuart Malcolm was booked for a rash challenge on Markus Paatelainen, but the Finn wasted the opportunity by firing the free kick straight at Creer as Alloa held on to record their first home league win of the season.