Alloa made a dream start, going in front on eight minutes. Ross Hamilton anticipated a pass from Steve Hamilton and was well placed to fire home from ten yards out.
Six minutes later Partick came close to levelling when a fierce shot from Scott Boyd from ten yards out rattled the crossbar and came back into play.
Thistle continued to press for an equaliser and came close in the 17th minute through Stephen McConalogue's shot and in the 22nd minute from a Billy Gibson header.
Against the run of play Graeme Brown doubled Alloa's lead on 30 minutes when he ran at the Thistle defence, beat Grant Murray then Boyd and sidefooted past Kenny Arthur.
Thistle fought back and were rewarded with a goal they deserved in the 37th minute when Dmytro Pronevych passed to Mark Roberts, who saw McConalogue in a scoring position and from 12 yards he drilled the ball past Allan Creer in the Alloa goal.
Partick threw everything forward, but the Alloa defence stood up to the test and the home side recorded only their second home win of the season.