The German record champions took the reins from the start whereas Monchengladbach implemented a wait-and-see strategy and lurked for counterattacks.
Bayern came close through Leon Goretzka, who tested Monchengladbach goalkeeper Moritz Nicolas with a header in the third minute while Sane pulled narrowly wide in the 19th minute.
Monchengladbach posed threat on fast breaks as Marvin Friedrich rattled the woodwork before Maximilian Wober flicked on a corner that allowed Ko Itakura to head home the 1-0 lead on the half hour mark.
The visitors had the opportunity to double their lead, but Sven Ulreich denied Julian Weigl’s low shot two minutes later.
After the half-time, Bayern started an onslaught on Monchengladbach’s goal but still neither Goretzka nor Thomas Muller could beat Nicolas from promising positions.
The German giants eventually got rewarded in the 58th minute when Joshua Kimmich chipped the ball into the path of Sane, who poked home the 1-1 equalizer from close range.
Monchengladbach couldn’t put up resistance while Bayern wasn’t done with the scoring and marked the 2-1 winner through joker Tel, who nodded home Kimmich’s pinpoint cross.
Elsewhere, Bayer Leverkusen maintain its perfect start into the season after the Werkself trashed newly promoted Darmstadt 5-1.
Werder Bremen secured its first win of the season as three second-half goals edged Mainz 4-0.
Stuttgart won the Southern derby after Serhou Guirassy provided a brace to see off Freiburg 5-0.
Hoffenheim came from behind to shock Wolfsburg 3-1 and Augsburg shared the spoils with Bochum following a 2-2 stalemate.
The following fixtures are scheduled for Sunday: Eintracht Frankfurt host Cologne and Union Berlin clash with Leipzig.
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