The visitors stormed into a 3-0 lead after 25 minutes but the prolific Dobbie handed Queens a lifeline with a quickfire double before the break and rounded off his treble in the second half to see the points shared.
Alloa claimed an early lead when Iain Flannigan slammed the ball high into the net and doubled their lead when Connor Shields’ cross was nodded home by Jake Hastie at the back post.
Remarkably Jim Goodwin’s side notched a third ten minutes later thanks to Shields’ looping header, but they couldn’t keep a clean sheet going into the break as Dobbie reduced the margin with a powerful effort into the top corner.
Dobbie had his second two minutes before half-time when he rifled a left-foot shot into the far corner and the comeback was complete when Dobbie’s low drive found the net for his 24th goal of the season. It was also the striker’s fourth treble of the campaign.