Anthony Martial opened the scoring in the 27th minute, his 50th goal for the club.
Wolves levelled in the 55th minute with a goal that survived lengthy VAR checks for offside, Ruben Neves smashing home a 20-yard drive after a clever set-piece routine.
A stretched finale saw chances at both ends, with Luke Shaw denied at the death as neither side could find a late winner.
With the draw, United missed going top of the league with a win. They have now failed to win any of their past five away games in the Premier League.