Wendell's fifth-minute penalty put Leverkusen ahead at Allianz Arena, with referee Tobias Welz having ordered the spot-kick to be retaken after Kevin Volland had missed his initial effort.
Bayern quickly equalised through Corentin Tolisso, however, and the hosts took the lead when Robben sensationally volleyed home in the 19th minute.
James Rodriguez wrapped up the three points a minute from time to maintain Bayern's winning start, after any hopes of a Leverkusen comeback bad been ended by a red card for substitute Karim Bellarabi.
Controversy reigned early on when Leverkusen was awarded a penalty after Thiago Alcantara handled, but Manuel Neuer pulled off a superb double stop to deny Volland from the spot-kick and resulting rebound.
Those saves would count for nothing, though, as the referee insisted that the penalty be retaken because of encroachment and Wendell made no mistake with his second attempt.
Leverkusen's lead was short-lived, however, Tolisso restoring parity in the ninth minute as he bundled his way through and steered a clever finish high into the right corner.
Bayern soon had the lead, with Robben latching on to a poor clearance before unleashing a wicked volley that dipped in over Lukas Hradecky, although Bayern was dealt a blow when Tolisso was forced off with a knee injury.
Leverkusen was toyed with for much of the second half and Bellarabi, only just on as a substitute, let his frustration get the better of him when he lunged in on Rafinha with 10 minutes remaining and rightly saw red.
Bayern made its numerical advantage count, James heading in from Thiago's cross to add further gloss to a comfortable victory, before having another effort ruled out for offside.
Both sides get their respective UEFA Champions League and UEFA Europa League campaigns up and running next time out. Bayern travels to Benfica, while Leverkusen faces Ludogorets.