The Reds' fifth straight victory also propelled them into the Championship play-off places.
Henri Lansbury scored either side of Matt Doherty's equaliser for Wolves, who were reduced to 10 men late on when Stephen Ward was shown a straight red card.
Substitute Lewis McGugan sealed the win in the final minute as Forest finished the day in sixth position.
Forest took the lead on 31 minutes. Former Wolves midfielder Adlene Guedioura was involved, teeing up Lansbury who arrowed a right-foot shot into the bottom left-hand corner from 20 yards out.
Sylvan Ebanks-Blake then won Wolves a free-kick 25 yards out. Bakary Sako took it and saw his crisp strike smash against the crossbar with goalkeeper Karl Darlow well beaten.
Bjorn Sigurdarson should have netted the rebound but blazed his shot high into the Bridgeford End, a terrible miss from the Icelander.
Wolves were working hard and they were rewarded with an equaliser after 65 minutes. Doherty's looping header from Sako's far-post cross had just enough on it to beat Darlow, who got his fingertips to the ball but could not keep it out.
However, their joy was shortlived as little more than 90 seconds later Lansbury curled in a lovely shot from the left-hand side of the box.
McGugan went close with a free-kick midway through the second half before Wolves' task increased in difficulty with Ward's red card.
Saunders' side went for broke at a corner, leaving only Ward back. Forest cleared the danger and counter-attacked with substitute Greg Halford, who was body-checked by Ward as he knocked the ball past the last man, leaving referee Michael Naylor with no option but to pull out a straight red card.
Forest made certain of all three points in the final minute, catching Wolves out with another swift turnaround.
A move involving Simon Cox and Gonzalo Jara Reyes culminated in McGugan curling in a shot via the crossbar from the edge of the area.