With three defeats in three, Leverkusen have made their worst ever start to a Bundesliga campaign.
Leverkusen got off to a dream start when Thiago's handball gave them a penalty in the second minute.
Manuel Neuer initially denied Kevin Volland from 12 yards, but the spot-kick was ordered re-taken for players encroaching into the area and Wendell smashed in the retake.
Leverkusen's joy was short-lived, as Corentin Tolisso prodded in the equaliser just four minutes later, and Robben fired Bayern ahead with a superb volley on 20 minutes.
"It wasn't easy today, but luckily we bounced back quickly," Robben told Sky. "I don't want to criticise my team-mates, but everybody needs to pull their weight when we are pressing."
Leverkusen's fate seemed sealed when Karim Bellarabi was sent off for a reckless challenge on Rafinha ten minutes from time, and James Rodriguez added Bayern's third in the 89th minute.
Champions League debut
Promoted Duesseldorf snatched a surprise 2-1 win over Hoffenheim, who make their Champions League debut next week.
Alfredo Morales headed Duesseldorf ahead against the run of play on the stroke of half-time. English youngster Reiss Nelson, on loan from Arsenal, appeared to save his team's blushes when he scored on debut to make it 1-1.
The relief did not last long, though, as Dodi Lukebakio restored Duesseldorf's lead from the penalty spot on 88 minutes.
Germany international Timo Werner scored twice to inspire RB Leipzig to their first win of the season in a 3-2 thriller against Hanover.
On his return to the starting eleven, Yussuf Poulsen nodded Leipzig ahead on ten minutes, before Niclas Fuellkrug blasted in an equaliser for Hanover a few minutes later.
Timo Werner twice linked up with Sweden striker Emil Forsberg on the counter-attack to put RB Leipzig 3-1 ahead, but the visitors were uncowed, and Miiko Albornoz quickly pulled a goal back with a curling shot into the top corner.
There was a flurry of late goals for Wolfsburg and Mainz, as Wolfsburg grabbed a late draw against Hertha Berlin and Mainz scored twice to snatch victory from the jaws of defeat against Augsburg.
After an uneventful first half, Javairo Dilrosun's well-angled finish broke the deadlock just after the hour mark, before Yunnus Malli equalised from the penalty spot three minutes from time.
Ondrej Duda appeared to have won it for Hertha with a direct free-kick moments later, but Admir Mehmedi prodded in another equaliser to rescue a point for the home side.
"The fact that we twice came back from behind against such a defensively strong opponent says a lot about my team," said Wolfsburg coach Bruno Labbadia.
After both sides had goals disallowed in the first half, the game was heading towards a goalless draw when Augsburg's Dong-won Ji sent the ball flying into the bottom corner.
Mainz though, hit back with goals from Anthony Ujah and Alexandru Maxim turning the game on its head in the last six minutes.