Bayern Munich conceded the joint quickest goal in Bundesliga history but turned it around and scored a last-minute winner in an action-packed game.
Kevin Volland seized on a misplaced David Alaba pass to put Hoffenheim in front after nine seconds, with Thomas Muller levelling soon before the break.
The hosts had a chance to beat Bayern for the first time ever when Jerome Boateng conceded a penalty for handball and was sent off, but Eugen Polanski hit the post with the kick and keeper Manuel Neuer landed on the rebound to keep it out.
Boateng’s dismissal was for a second booking – having also been shown a yellow card for another handball 90 seconds earlier.
And substitute Robert Lewandowski scored the 90th-minute decider from Douglas Costa’s cross.
Summer signing from Juventus, Arturo Vidal, and reported Manchester United target Muller both hit the woodwork.
Bayern have won both their opening games, as have Bayer Leverkusen, the only two teams on six points.
Borussia Dortmund play Ingolstadt on Sunday, with both sides having won their opener.
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