United were helped when Forest had Yohan Benalouane sent off two minutes into the second half.
United went into the game on the back of just one win in their last four matches, desperately needing a victory to boost their chances of securing automatic promotion.
Oliver Norwood tried an early effort for the home side, sending a long-range shot wide of the target.
Claudio Yacob had the first sight of goal for visitors Forest when he saw his fierce drive miss the target from 25 yards.
Forest’s Jack Colback was then shown a yellow card for simulation when he went down in the area following a challenge from George Baldock.
The hosts had a decent spell of possession, with Stevens’ delivery from the left posing problems for the opposition.
First, Stevens whipped in a low, in-swinging cross, which just evaded Gary Madine.