Bayern lost the first leg 3-2 to Paris Saint-Germain on Wednesday.
Marcus Ingvartsen scored late for Union Berlin to grab a 1-1 draw and cut Bayern Munich's Bundesliga lead on Saturday ahead of Bayern's decisive Champions League game in Paris on Tuesday.
Union's visit came at the wrong time for the European champion, weakened by injuries and focused on the second leg in the quarterfinals of the Champions League. Bayern lost the first leg 3-2 to Paris Saint-Germain on Wednesday.
Bayern struggled to break through Union's stubborn defense until the 18-year-old Jamal Musiala finally made the breakthrough in the 68th minute, but Robert Andrich set up Ingvartsen for the visitors' equalizer in the 85th.
Leipzig cut Bayern's lead to five points with six rounds remaining with a 4-1 win at Werder Bremen.
Bayern coach Hansi Flick, who said Friday his squad wasn't as strong as the previous year's, started with reserve players Josip Stanisic and Tiago Dantas. It was a debut for the 21-year-old Stanisic, a defender, and first start for Dantas.
Bayern's injury worries deepened after about half an hour when Kingsley Coman needed treatment on his left knee, but the France attacker continued till the break, when he was substituted by Leroy Sané.
The 18-year-old Christopher Scott came on for his Bayern debut in the 66th, and Musiala scored two minutes later. Union's defense failed to clear the ball, which rebounded off Thomas Müller's shoulder into Musiala's path. He danced past a couple of defenders before scoring from close range.
Ingvartsen's equalizer cost Bayern two points, however, and kept Union flying high in seventh place.
Fourth-place Eintracht Frankfurt enjoyed a 4-3 win over third-place Wolfsburg, and Hertha Berlin could only draw 2-2 with Borussia Mönchengladbach despite playing most of the game with a player advantage after Yann Sommer's early sending off for the visitors.
