.
Henrikh Mkhitaryan and Pierre-Emerick Aubameyang scored early to give the visitors a 3-1 aggregate lead.
Divock Origi slotted in to pull one back for Liverpool only for Marco Reus to fire in for Dortmund.
Philippe Coutinho and Mamadou Sakho goals gave the Reds hope before Lovren headed in for an epic victory.