All the goals arrived in the second half when the hosts took control of the game after Mainz kept them at bay successfully for 45 minutes.
Riccardo Rodriguez scored the first from the penalty spot before Bas Dost added a second. Luiz Gustavo added a third to reinforce the Wolves' place inside the top six.
The first half was as dismal as the weather at the VW-Arena with the hosts endeavouring to break a defensive Mainz down, but failing to find a way through.
Kevin De Bruyne was at the centre of all their attacks, but Mainz had already earmarked him as the dangerman and were doubling up in their marking of the Belgium international.
As it was, Mainz created the two best chances of the half with former Wolfsburg midfielder Ja-Cheol Koo just missing the target with a chance before Eric-Maxim Choupo-Moting sent a shot over the crossbar from a good position.
Early in the second half, Maximilian Arnold tested Loris Karius with a shot from 20 yards which the Mainz goalkeeper did well to keep out low down at his left-hand post.
Wolfsburg had clearly stepped up a gear and they finally got the break they were looking for when Dost was brought down by Stefan Bell just as he was entering the penalty area.
The referee pointed to the spot and, after Dost left the field limping, Rodriguez stepped up to break the deadlock.
Dost was supposed to be replaced by Olic, but he signalled that he could carry on and the Croatian instead took the place of Ivan Perisic.
It proved to be a wise move too with Olic setting Dost to make it two in the 66th minute, playing him in on the edge of the penalty area, from where the Dutchman kept the ball low with his shot into the bottom left-hand corner.
Mainz seemed to give up at that stage and they were punished further when they left Luiz Gustavo unmarked to make it three in the 75th minute.