.The Bundesliga champions, who lost only once last season, in the Europa League final against Atalanta, netted early on through Germany international Wirtz.
Spain's Alejandro Grimaldo made it 2-0 on the half hour and playmaker Wirtz soon scored a near carbon copy goal, with Dutchman Jeremie Frimpong again assisting.
An own goal from Feyenoord's German goalkeeper Timon Wellenreuther had Leverkusen four up on 45 minutes.
"Compliments to the team for playing like that against a good side," Leverkusen midfielder Granit Xhaka told DAZN.
"4-0 away from home, we will definitely take that. The fans here are unbelievable, it's a great atmosphere but we made them quieter."
In the other early game, Benfica beat fellow former winners Red Star Belgrade 2-1 in Serbia thanks to the Turkish duo of Kerem Aktürkolu and Orkun Kökçü, the latter of whom dispatched a perfect free-kick.
Felício Milson pulled one back four minutes from time.
Later matches are: Atletico Madrid v RB Leipzig, Atalanta v Arsenal, Monaco v Barcelona and European debutants Stade Brest v Sturm Graz.
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