Bayer gets big win over Frankfurt
Visiting fans lit flares and fireworks after 15 minutes to prompt an unscheduled break in the game, as the players were taken off the pitch.
Leverkusen returned to the field to provide pyrotechnics of their own with goals from Sebastian Boenisch and Stefan Kiessling.
Andre Schurrle made it 3-0 in the 58th minute before Alexander Meier grabbed a late consolation for Armin Veh's men, who remain fourth in the table.
Diego and Alexander Madlung scored the goals, both in the second half, as the Wolves moved clear of the bottom three in the Bundesliga and to within three points of their opponents.
In an even-match, two defensive mistakes cost the visitors dear as they succumbed to a defeat which leaves them two points adrift of the top six.
The game came to life late on when Mainz went closest to breaking the deadlock, but they were also forced to end the game with 10 men after Shawn Parker picked up a second yellow card late on.
The two surprise packages from the first half of the Bundesliga season were therefore able to remain in the hunt for a Europa League place.
Kurz, who took charge of the beleaguered Bundesliga side during the winter break, set his side up with caution in mind, and although they created few goalscoring openings, they conceded even fewer chances.
Gladbach, for their part, looked equally happy to come away with a point, which leaves them in eighth.