There was a flurry of late goals in other games including two in the last 10 minutes as Fortuna Duesseldorf beat Hoffenheim 2-1, three in VfL Wolfsburg's 2-2 draw with Hertha Berlin and three more in Mainz 05's 2-1 win over Augsburg.
Bayern's win ensured that the Bavarians, aiming for a seventh successive title, were the only team on nine points after their opening three games.
Wendell gave Leverkusen a fifth-minute lead, scoring from a penalty after Kevin Volland missed the first attempt but was reprieved when the referee ordered a retake. Bayern, though, needed only five minutes for Corentin Tolisso to equalise.
Robben put Bayern in front nine minutes later and substitute James Rodriguez headed the third goal with a minute left.
(Writing by Brian Homewood; editing by Clare Fallon)
