The Blades' winless run under Adams looked set to be extended to 14 games when Dele Adebola gave Forest the lead just before half-time.
But they rallied in the second half and despite Daniel Bogdanovic having a penalty saved by Lee Camp, United secured their first Championship win since December 18 courtesy of on-loan striker Sam Vokes' first goal for the club and a Matt Lowton header.
The victory boosts the Blades' hopes of avoid relegation, while Forest are without a win in five games as their hopes of finishing in the top two suffered another setback. The Blades fashioned the first opportunity when striker Bogdanovic did well to pick out the onrushing Stephen Quinn, but the midfielder took a heavy touch as he surged into the penalty area and the chance was gone.
Both sides struggled to keep hold of the ball in a drab first half but United fashioned another half-chance 13 minutes in when Richard Cresswell crossed from the right and Quinn stabbed his shot wide at the far post.
Former Sheffield Wednesday Marcus Tudgay had a chance to silence the Blades fans who booed his every touch but the forward fired his right-foot strike wide from just outside the area in the 29th minute.
It just as the first half seemed destined to finish goalless Forest took the lead four minutes before the break with a goal out of nothing.
The United defence allowed the ball to bounce in the penalty area and Adebola used his considerable frame to control the ball on his chest and spin his marker then tuck the ball home with his left foot from six yards out.
Cresswell spurned an excellent chance to equalise three minutes into the second half when the ball bounced nicely for him in the penalty area but he scuffed his shot wide.
But United must have thought their luck was to change after 65 minutes when Chris Gunter upended Bogdanovic and referee Tony Bates pointed to the penalty spot.
Bogdanovic picked himself to take the resulting spot-kick but Camp guessed the right way and palmed away his tame right-foot effort.
Forest boss Billy Davies brought on new signing Kris Boyd for Adebola with 20 minutes remaining, but two minutes later United were level when Vokes broke into the penalty area and tucked the ball under Camp with a composed right-foot finish from a tight angle.
And there was worse to come for Forest when Quinn swung a corner over from the left nine minutes from time and Lawton rose to plant a header beyond Camp and leave Bramall Lane rocking.