Bayern beat Wolfsburg with late winner
Bayern, who were missing injured winger Arjen Robben and striker Ivica Olic, were the livelier side early on, with Franck Ribery in superb form.
With Germany coach Joachim Low in the stands and the game seen in 197 countries, World Cup joint top scorer Thomas Muller fired the hosts into the lead in the ninth minute after combining beautifully with Toni Kroos.
Last season's Bundesliga top scorer Edin Dzeko grabbed a deserved 55th-minute equaliser for Wolfsburg when he headed in a Zvjezdan Misimovic corner to give fired-up former England coach Steve McClaren a reason to smile on his Bundesliga debut.
Bayern hit back deep into added time when an unmarked Schweinsteiger tapped in a Ribery cross at the far post.
"A win and three points make me happy," said Bayern coach Louis van Gaal.
"For the first 15 minutes of the second half we just gave away too many balls. But then we were good and Ribery played for 90 minutes. That's unbelievable," he said of the Frenchman, who spent much of last season injured.
Van Gaal opted for a new-look central defence with Holger Badstuber partnering Daniel van Buyten, leaving out Argentine Martin Demichelis, who angrily refused to sit on the substitutes' bench before the start of the game.
Ribery looks to have hit top form at the right time and was a constant threat with furious runs down the left wing and some pin-point passing.
Yet it was Kroos, back this season after his loan spell at Bayer Leverkusen, who set up Mueller for the first goal.
Diego Contento came close to adding another when Ribery fed him inside the box but the defender was denied by Wolfsburg keeper Diego Benaglio.
McClaren brought on playmaker Misimovic in the second half to add pace and precision in midfield and two minutes after the restart Croatian Mario Mandzukic rattled Bayern's post with a beautifully-curled, low shot.
Dzeko saw his drive sail just wide a minute later as Bayern looked out of sorts.
McClaren, whose last encounter with Bayern was as a Manchester United assistant coach in their victorious 1999 Champions League final, was by now on his feet, yelling at his players to keep pressing.
They did just that and it was Dzeko who delivered when he rose above Van Buyten to head in the equaliser.
With Wolfsburg stretching forward for the winner, the hosts hit back in the dying seconds when Ribery sailed a deep cross from the left to Schweinsteiger, who tapped it in.
"We did not deserve that," McClaren told reporters. "We could have won this game."