The new-old German champion is facing a Champions League rematch against PSG on Wednesday, so Vincent Kompany sent a combined team onto the field.
The guests led 2:0 after half an hour with goals from Zivzivadze and Dinkchi, before Goretzka scored from a free kick in the 44th minute.
The same player brought the Bavarians an equalizer in the 57th minute, but Zivzivadze silenced the Allianz Arena with his second goal of the match in the 76th minute.
Bayer then attacked violently, and then in the 10th minute of injury time, after a shot by Olis, the ball hit the post and bounced off goalkeeper Ramaj into the net.
Heidenheim thus remains in last place with 23 points, three less than St. Pauli, which is in the play-off zone.
The Hoffenheim – Stuttgart duel also ended with the identical result as the one in Munich.
The home team led 2:0 and 3:1, and had a player more in the last 20 minutes (Cazaror was sent off), but the "Straits" did not give up, and Thomas brought a point to Stuttgart in the fifth minute of injury time. The two teams are tied for fourth place, with the "Straits" having the better goal difference.
In the remaining matches, HSV surprised Frankfurt away (2:1), Augsburg was better than Werder Bremen away (3:1), while Union and Cologne drew (2:2).
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