Wendell's fifth-minute penalty put Leverkusen ahead at the 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 were 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 due to encroachment and Wendell made no mistake with his 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 were dealt a blow when Tolisso was forced off with a knee injury.
Leverkusen were 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.
And Bayern made their 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.
What it means: Bayern roll on under Kovac
It has been a perfect start for Niko Kovac, whose Bayern side have easily overcome every challenge thrown their way so far. Leverkusen, meanwhile, are rooted to the foot of the table without a point.
Pat on the back: Evergreen Robben imperious
While Leverkusen star Julian Brandt failed to shine, Robben reigned supreme down the same flank, capping his performance off with another memorable goal - his 97th in the Bundesliga and 140th for Bayern in all competitions.
Boot up the backside: Volland's goal drought continues
Volland scored 14 Bundesliga goals last term, but is still in search of his first this season. The striker's penalty was poor, and to make matters worse he failed to beat Neuer from point-blank range on the rebound.
Key Opta stats
- Bayern have won each of their five games in all competitions under Niko Kovac. Carlo Ancelotti started with 8 wins in a row.
- Arjen Robben scored his 140th goal in all competitions for Bayern, the only foreign player with more goals for Bayern is Robert Lewandowski (157 goals). Robben had twice as many shots in the game as opponent Leverkusen (6-3).
- Lewandowski made his 200th appearance in all competitions for Bayern, but fired only one shot which was blocked.
- For the first time in their Bundesliga history, Leverkusen lost the opening three games.