After a goalless first half, it slammed four times in the second.
Bayern Munich took the lead in the 57th minute after an own goal by an Ajax player.
Just over ten minutes later, Sydney Lohmann also came 2-0.
Ajax reduced with ten minutes left but the guests got the last word.
In the 86th minute, Simone Laudehr put 3-1 which was the end result.
Bayern Munich thus has an excellent starting position for the return at home on 16 December.
Swedish national team duo Amanda Ilestedt and Hanna Glas played from the start for Bayern Munich.
Glas played the whole match while Ilestedt was replaced at the break.