Both sides will feel they should have picked up a badly needed victory as Wolves held the edge in the opening period before United moved up a gear to dictate the second half.
But a real cutting edge was lacking with goal-shy Wolves continuing to look lightweight in attack and United badly missing their injured 13-goal leading scorer James Beattie.
United handed an instant bow to Gary Speed after his arrival from Bolton and he was agonisingly close to making a dream debut after just five minutes, when only a full-length flying save by Wayne Hennessey denied him a goal.
It was something of a false dawn for United as Wolves went on to carry the greater threat in a low-key first half that struggled to come to life.
Andy Keogh saw a deflected 11th minute shot comfortably saved by Paddy Kenny before Neill Collins headed a Jay Bothroyd free-kick over the bar two minutes later.
While Karl Henry had a shot blocked by Speed in the 29th minute, Wolves looked most dangerous from set pieces and they should really have broken the deadlock on the stroke of half-time.
Once again, Bothroyd's delivery, this time from a corner, picked out the unmarked Collins, but the Scotsman was unable to keep his header down and it flew just over the bar.
Having weathered the best that Wolves could throw at them, United grew in confidence after the break and created three gilt-edged chances.
Jon Stead was inches wide from the edge of the area in the 54th minute before Lee Hendrie was denied by another smart Hennessey save after Collins' clearance had cannoned into his path off Darren Ward.
Rob Hulse was then just off-target from 20 yards before Wolves created their only chance of note in the second period.
A neat pass from Seyi Olofinjana released Bothroyd after 76 minutes, but he could not find a way past Kenny who bravely dived at the feet of the well-travelled marksman.