Victor Moses put the struggling Latics ahead on the stroke of half-time, but Gary Caldwell was then sent off for deliberate handball in the 76th minute and Jonathan Walters converted the resulting penalty to draw eighth-placed Stoke level.
When substitute Cameron Jerome - whose header had led to Caldwell's dismissal - subsequently put the hosts ahead, things looked bleak for Wigan, but Watson then scored an 87th-minute penalty of his own - with his first touch - after Ryan Shotton had been penalised for a tug on Hugo Rodallega's shirt.
Source: PA
Source: PA