Centre-back Joleon Lescott struck in the 87th minute as managerless Wolves snatched a vital point.
The Midlands side with Harry Redknapp firm favourite take over next week had snatched the lead in the eight minute, striker Seyi Olofinjana ideally placed to run on to Colin Cameron's deflected cross as the Nigerian hammered the ball past Paddy Kenny.
Paul Shaw, replacing the injured Danny Cadamarteri, blundered in the 18th minute as he tried to connect with Michael Tonge's precise pass, but miscued from 12 yards.
Tonge produced a spectacular overhead kick minutes later but volleyed over as the Sheffield side pressed for an equaliser.
It came in the 28th minute, Andy Liddell's corner was cleared to the lurking Leigh Bromby on the edge of the area, who coolly chested the ball down before cracking his half-volley into the top corner, for his third of the season.
Carl Cort hit the United woodwork minutes after the interval before snatching the lead in the 51st minute, drilling Cameron's left-wing cross past the United keeper from 16 yards.
United were back on level terms just two minutes later, midfielder Paul Thirlwell grabbing his first for the club with a right-foot shot from the edge of the area.
Wolves keeper Michael Oakes brought off a stunning save in the 66th minute finger tipping Jon Hartley's curling free-kick round the post.
Shaw grabbed United's third tucking the ball beyond Oakes' reach 17 minutes from time, before Lescott had the final word with three minutes to go.