Donovan, who formerly played in Germany for Bayer Leverkusen, dribbled the ball to the top of the box before blasting it past German World Cup goalkeeper Manuel Neuer in the 70th minute.
The Bundesliga champions had seven members of the World Cup-winning German national team, but most of them remained on the bench until about the final 10 minutes.
Bayern's new signing Robert Lewandowski opened the scoring for the Bavarian club early in the first half before Bradley Wright-Philips equalized early in the second.
Bayern coach Pep Guardiola said he was only playing his World Cup players for some 15 minutes apiece to freshen them up for the approaching German and European seasons and he was true to his word. None of them started on Wednesday.