Wolves led through Pedro Goncalves’s superb goal on 66 minutes and struck the Stoke crossbar three times.
But after some late Stoke pressure, a handball by Cameron John in the second minute of stoppage time handed the Potters a chance to end a four-match losing streak and Campbell duly took it.
Wolves remain five points behind the play-off places, while Stoke are second bottom with 10 points.
Wolves: 22 Jan v Bury (H) PL Cup
Stoke: 19 Jan v Bristol City (H) PL Cup