Bayern, which lost at home to Bayer Leverkusen last weekend, dominated the first half but could not open the scoring until shortly after the restart, Ivan Perisic on target with a fine finish.

Its lead was short-lived at Borussia-Park, however, as Bensebaini's header drew Gladbach level within 11 minutes to set up a gripping finale.

Javi Martinez conceded a late penalty for fouling Marcus Thuram - and was sent off - with Bensebaini staying cool to beat Manuel Neuer and leave Bayern seven points behind leaders Gladbach.