The hosts produced as many as 35 goal attempts, 20 of which were on target, but they managed to beat Sommer just once.
Bayern Munich were dominant in the first half, but they lacked a clinical touch in front of goal.
Meanwhile, Borussia Monchengladbach‘s Marcus Thuram took their only chance just before half time to take the Bavarians by surprise.
Julian Nagelsmann‘s men hit the ground running in the second half too, but they wasted numerous chances to equalise in their bid to turn the game around.
Sommer pulled off as many as 19 saves throughout the 90 minutes, but he couldn’t stop Leroy Sane with seven minutes to go.
The former Manchester City forward levelled the scores and Bayern Munich missed a couple of fine goal opportunities in the remaining minutes, with Sommer denying both Alphonso Davies and summer signing Matthijs de Ligt.
Bayern Munich dropped points after registering three wins in which they scored 15 times and conceded three goals.
They remain top of the table along with Union Berlin, while Borussia Monchengladbach are currently sixth with eight points.