The first real chance of the match arrived after five minutes when Philippe Coutinho fed Raheem Sterling inside the box, but the England international's effort was straight at Mitchell Langerak, before Jordan Henderson clipped one high of the crossbar.
Liverpool were ahead five minutes later, however, when Daniel Sturridge finished into the bottom corner with the outside of his foot.
It was 2-0 after 14 minutes when Dejan Lovren headed home from a corner on his home debut.
The hosts continued to dominate and forced another chance after 20 minutes, but Coutinho's effort whistled wide of the post as Dortmund struggled for possession of the ball.
Steven Gerrard had the final chance of the half, but his free kick was pushed wide by Langerak.