The Werkself assumed control from the starting whistle but had to wait until the 22nd minute before Wirtz rattled the left post after Granit Xhaka's chip into the box.
Wolfsburg also came close three minutes later after Leverkusen goalkeeper Lukas Hradecky had to defuse Cedric Zesiger's 20-meter attempt.
The game tilted further in Leverkusen's favour 28 minutes in when Wolfsburg's Moritz Jenz was sent off for receiving a second yellow card. Leverkusen capitalized on the one-man advantage, opening the scoring in the 37th minute through Nathan Tella, who headed in Alejandro Grimaldo's precise cross.
Wolfsburg had his hands full of work and was lucky in the 40th minute when custodian Koen Casteels neutralized Piero Hincapie's dangerous header.
In the second half, Leverkusen maintained their dominance, opting for shots from distance that failed to surprise Casteels. However, they sealed the victory in the 86th minute when Wirtz finished off Exequiel Palacios' excellent pass at the far post.
"It is tough to play against Leverkusen with eleven players, so the game was basically over after the dismissal. We played well until the sent off, but we must get our points from somewhere else," said Wolfsburg coach Niko Kovac.
"We started well. It was important to score after the sent off and to remain patient. We are delighted with the result," commented Leverkusen coach Xabi Alonso.
In other Bundesliga action, Freiburg ended their six-match winless streak with a 2-1 victory over Bochum, thanks to goals from Maximilian Eggestein and Michael Gregoritsch, while Eintracht Frankfurt defeated Hoffenheim 3-1.