Both sides remain six points adrift of Chelsea, despite a run of four wins in 13 games for the Blues, and fall a point behind Sheffield United.
United handed a debut to £47 million ($62 million) signing Bruno Fernandes in midfield as he went head-to-head with a host of his Portuguese international teammates.
Fernandes has been recruited to add some much-needed guile and goals to the United midfield and a lack of creativity and cutting edge upfront without the injured Marcus Rashford was evident as they failed to break down a well-organised Wolves.
United’s new signing Odion Ighalo is yet to arrive in the club so he was unable to feature in the Saturday’s encounter.
Ole Gunnar Solskjaer’s men were largely limited to shots from range with Fernandes keen to make his mark.
Andres Pereira and Fernandes fired wide before the debutant’s clean strike from the edge of the box was too close to Rui Patricio.
Wolves also harbour ambitions of playing Champions League football for the first time next season, but were overly cautious in their approach and have now failed to score in three meetings with United over the past month.
Adama Traore caused Liverpool a litany of problems in Wolves last outing, but the Spaniard was not allowed the same space to exploit by United and blasted wide his side’s best chance before the break.
Fernandes tested his former Sporting Lisbon teammate Rui Patricio again from distance with a free-kick and Juan Mata curled wide as United’s pressure began to build without ever cutting the visitors’ open.
And Wolves’ plan to contain and counter-attack nearly paid off when Traore burst through the heart of the United midfield and played in Raul Jimenez, who forced David de Gea into a fine save.
United’s other new signing Odion Ighalo was not available after completing a late loan move from Shanghai Shenhua before Friday’s transfer deadline.
Solskjaer, therefore, had to turn to 18-year-old Mason Greenwood in the search for a winner and the teenager nearly delivered with a deflected shot that fell kindly into the wrong-footed Patricio’s arms.
The hosts best chance fell to substitute Diogo Dalot deep into stoppage time, but his header trickled inches wide to ensure United have won just one of their last five league games.