But Hamit Altintop levelled, following up after his penalty was saved, after Spanish referee Eduardo Iturralde Gonzalez had penalised Alan Maybury for handball despite previously ignoring two similar Aberdeen appeals.
The decision deprived the Dons of the chance to hold on for another win over Bayern, who lost 3-2 at Pittodrie during the home side's triumphant European Cup Winners' Cup campaign in 1983.
Aberdeen manager Jimmy Calderwood appreciated the way Bayern improved in the second half, but he was full of praise for his own side's display.
"It was a wonderful performance in the first half, the whole game really," Calderwood said.
"They upped the tempo a little bit in the second half, bringing the boy (Philip) Lahm on, he caused us problems."
The disappointment for Calderwood was that Bayern got two away goals, which in the case of a low-scoring draw next week could be decisive.
"We wanted to keep a clean sheet," he said.
"They are a quality team. We were disappointed with their goals. We've had to work hard. We got two wonderful goals to get ours."