Wolves, who had strong claims for a penalty turned down in the 54th minute when Kyel Reid looked to have been fouled by Jamie Mackie, only had themselves to blame for this setback.
They camped out in the Pilgrims half for the second period but couldn't test goalkeeper Romain Larrieu.
Plymouth had won just one of their previous 16 games but they mounted a superb rearguard action with left-back Chris Barker and central defender Craig Cathcart particularly impressive.
Wolves have shown a tendency to concede early goals this season, but plumbed new depths against Plymouth.
They really were caught cold when Barker launched a long throw into the Wolves area.
Jamie Mackie helped the ball on and Gallagher pounced to let fly with an overhead kick that flew past the outstretched left hand of Wayne Hennessey for his ninth goal of the season.
Wolves did make a determined bid to grab an equaliser before half-time but their finishing was far from clinical.
Andy Keogh again toiled in front of goal seeing his close-range shot blocked by Cathcart before he failed to get on the end of a teasing cross from Michael Kightly.
Kightly then had a drive smothered by Barker with Reid's follow-up shot comfortably saved by Larrieu.
Having successfully weathered that Wolves storm, Plymouth were unfortunate not to take a bigger advantage into the break.
Fletcher's 29th minute drive whistled just wide before Hennessey dived bravely at the feet of Ashley Barnes ten minutes before half-time.
For all the pressure that Plymouth then faced in the second half they could have made the game safe on the hour after a mistake by Christophe Berra.
His misplaced clearance was pounced on by Barnes, who then teed up Gallagher to let fly with a 20 yard drive that whistled just past the post.
Wolves dismal day was summed up 16 minutes from time by their Plymouth old boy, 21-goal striker Sylvan Ebanks-Blake.
He was released by David Edwards and only had Larrieu to beat but sliced his shot horribly wide from 12 yards.