Midfielder Kimmich snatched the ball in midfield, played a one-two with Robert Lewandowski and had his shot blocked before the ball bounced back off his foot and into the net.

"It was not that easy especially in the second half. We led 2-0 but then made our own life difficult," said Bayern coach Hansi Flick, who took over in November and has enjoyed a sensational 10 months in charge.

"What counts is that we won the game. Everything else we will need to do better on Sunday (against Hertha)," he added.

Bayern, eager to bounce back from Sunday's shock 4-1 loss to Hoffenheim which snapped their 32-game unbeaten run, quickly raced into a 2-0 lead with goals from Corentin Tolisso in the 18th minute and Thomas Mueller in the 32nd.

Dortmund battled back with a goal from Julian Brandt before Thomas Meunier missed a golden chance to level with only Manuel Neuer to beat but the defender sent his shot well over the bar.

Erling Haaland did better in the 55th minute and should have scored again when he was sent through. Neuer stood his ground, however, to deny the Norwegian and Kimmich snatched the winner.

Bayern have also won the German league and Cup double, the Champions League and the European Super Cup this year.

Australian Associated Press