After the win on Tuesday (Wednesday AEDT) they are second in the standings, one point behind Bayern, who host Hoffenheim on Thursday (AEDT).
Leverkusen failed to find a way through in-form Mainz in the first half, but Alex Grimaldo took a free kick up and over the Mainz wall to finally break the deadlock in the 48th minute.
The goal secured Leverkusen a seventh straight league win and 10th in all competitions.
"We're in good form at the moment, everything is going the way we want. Today was tight, but luckily only one goal was enough," striker Patrik Schick told Sky.
Elsewhere, promoted Holstein Kiel had to endure Borussia Dortmund's late comeback attempt but held on to claim a 4-2 win.
The home crowd in Kiel was euphoric when Shuto Machino broke the deadlock in the 27th minute, but there was more to celebrate when Phil Harres added a second in the 32nd and Alexander Bernhardsson was also on target before the break.
Phil Harres celebrates after scoring Kiel's second goal in their 4-2 win against Borussia Dortmund. (AP PHOTO)
Giovanni Reyna in the 71st and Jamie Gittens in the 77th put Dortmund back in the fight.
Luck seemed to be on Dortmund's side when Lewis Holtby was sent off in the 86th minute, but Kiel sealed the victory in the eighth minute of stoppage time.
Goalkeeper Gregor Kobel went up for a late corner for Dortmund, but was left stranded and couldn't catch Fiete Arp, who raced forward and slotted the ball into the empty net.
Dortmund have struggled when playing away from home, with only one win from their eight games as guests. They sit ninth in the standings, while Kiel are in the relegation zone in 17th.
"We're not getting it right. We didn't have any goalscoring opportunities today, we just passed the ball back and forth," Dortmund midfielder Emre Can told broadcasters Sky.
In Frankfurt, the home side fell behind 1-0 against Freiburg when Ritsu Doan scored the opener for the guests in the 37th minute, but were quickly level as Robin Koch glanced Omar Marmoush's corner into the goal in the 43rd.
That was followed by a superb performance in the second half, with Marmoush getting one himself in the 65th in what might have been his last game for Frankfurt amid rumours he's set for a transfer to Manchester City.
Hugo Ekitike in the 71st and a late effort from Nnamdi Collins secured the win, with Frankfurt sitting in third place in the table.
In the other match, VfL Wolfsburg thrashed Borussia Monchengladbach 5-1. Jonas Wind broke the deadlock in the third minute from the spot, and Joakim Maehle, Maximilian Arnold and Lukas Nmecha (twice) were on target in the second half.
 Shio Fukuda pulled one back for Monchengladbach in the 89th minute.
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