Erik ten Hag's side were pushed all the way in M16, but could have gone ahead after just 10 minutes played, with Marcus Rashford's strike denied by Jose Sa.
Wolves had their chances, with Matheus Cunha presented with the visitors' best opening of the game shortly after the restart. Pedro Neto's low cross eventually found the unmarked Portuguese playmaker at the back post, but he could only steer his strike onto the woodwork and wide.
The Reds soon made Gary O'Neil's side pay, as Aaron Wan-Bissaka picked out Varane inside the penalty area, who nodded home the game's only goal to secure our opening-day success.