Chances were at a premium during the opening 45 minutes at Old Trafford, and it was Wolves who came closest to an opener on the counter-attack as Matheus Cunha drove forward and played in Pablo Sarabia, whose effort went just wide.
Both sides could have scored in an open start to the second half.
Four minutes after the break Cunha, who had been a threat throughout, missed a gilt-edged chance as he hit the post at close range. At the other end, a lobbed effort from Antony was headed off the line by Craig Dawson.
Wolves continued to look the more threatening side but were wasteful with their finishing. Their total of 23 shots was the second-most by a visiting team to Old Trafford in the Premier League since 2003/04, while their six shots on target without scoring were the most at Man Utd for four years.
They were punished in the 76th minute as United went ahead against the run of play.
Aaron Wan-Bissaka's floated cross was met by fellow defender Varane, who nodded into an open net at point-blank range to score his first goal in 26 Premier League matches, since netting against Brentford in May 2022.
Wolves appealed for a penalty in stoppage time as Onana clattered into Sasa Kalajdzic, but their claims were waved away by referee Simon Hooper.
Wolves' six shots on target without scoring were the most by a visiting Premier League side at Old Trafford for four years, as Onana became the 11th goalkeeper to keep a clean sheet on his Premier League debut for Man Utd, and the first since Joel Pereira in May 2017.