The German champions took a fifth-minute lead when Wirtz placed the ball into bottom corner from 20 yards.
Xabi Alonso’s marauding wing-backs combined for the second goal as Jeremie Frimpong’s cross reached Alex Grimaldo to score.
Former Celtic player Frimpong then picked out 21-year-old Germany international Wirtz, who volleyed in his second of the game.
And Leverkusen had the game won before half-time when Edmond Tapsoba’s header was knocked into his own net by home goalkeeper Timon Wellenreuther.
It was a clinical performance from the Bundesliga side, who had fewer shots than Feyenoord.
This was the Dutch side’s first defeat since Dane Brian Priske replaced Liverpool-bound Arne Slot as manager in the summer.
© BBC.