Oliver Norwood put the Reds ahead from the penalty spot, but a goal in each half from Nathaniel Mendez-Laing saw Wolves come away from Carrington with the points.
Paul McGuinness' men were awarded an early spot-kick when Paul McCone handled Nicky Ajose’s goalbound shot. Captain Norwood, who scored the only goal of the reverse fixture between these sides in October, stepped up to beat Wolves keeper Daniel Wright.
But Wolves equalised when a long throw caused chaos in the United defence and Jack Price's shot rebounded into the path of Mendez-Laing, who finished low beyond Gary Woods.
And England U17 international Mendez-Laing grabbed the winner after the break, receiving the ball from substitute Krisztian Smith after a flowing Wolves move, bursting away from two United defenders and firing a shot which deflected off the sliding Scott Moffatt and over Woods into the net.
United almost snatched a share of the spoils late on, but substitute John Cofie's header from Norwood's inswinging corner hit the bar.
United: Woods, Strickland, Dudgeon, Fryers (Moffatt 46), Wootton, Norwood, Curran (Cofie 63), Tunnicliffe, Brandao, Ajose, Galbraith (Morrison 46).