Robbie Kruse claimed a double with Lars Bender and last season's Bundesliga top-scorer Stefan Kiessling completing the rout, condemning Mainz to a third straight defeat after they had won their opening three games of the season.
Yunus Malli scored a consolation for the hosts in the 82nd minute, but their early-season glory is now a distant memory.
Simon Rolfes at one end and Eric-Maxim Choupo-Moting at the other sent shots over the bar before Kruse gave the visitors the lead in the 19th minute.
Sidney Sam turned on the turbo before squaring the ball to Kruse, who had managed to keep up with him and also kept a cool head to beat Heinz Muller with the outside of his boot.
It was the first goal for Leverkusen for the former Fortuna Dusseldorf forward, who was picked ahead of Heung-Min Son for his first start of the season.
Bender went close to making it two as Leverkusen stamped their authority on the game, the midfielder getting their second goal in the 38th minute with Kruse the provider.
The Australian squared the ball for Bender, who was left room to shoot from 25 yards and the ball beat Muller thanks also to a deflection off a Mainz defender.
Before the break, Leverkusen added a third, practically ending the contest with Kruse again showing an excellent eye for goal with a precise shot into the far corner.
Kiessling got in on the act on the hour mark, using his full frame to reach Simon Rolfes' cross with a diving header which nestled in the right-hand corner of Muller's goal.
Leverkusen took their foot off the pedal and Mainz took advantage when it was already too late, Malli volleying the ball in after Philipp Wollscheid's attempted clearance fell nicely for him.