Bayern had not been beaten away from home in the Champions League since 2017 when an Unai Emery-managed Paris Saint Germain saw them off.
Twenty five games later they were beaten again by the coach who turned down Newcastle earlier in the season because he felt he had unfinished work with Villarreal.
Villarreal are the first side to keep a clean sheet against Bayern Munich in the UEFA Champions League since Liverpool in February 2019, ending a run of 30 consecutive games in which the German side had netted at least once.