The Belgian striker, starting for the Reds in place of Daniel Sturridge, put the visitors ahead after 36 minutes with a cool finish past Weidenfeller.
James Milner’s header found Origi on the edge of the box, whose sliding finish took a slight deflection to beat the Dortmund shot-stopper, rolling into the bottom corner.
It was just his fifth goal for Liverpool, perhaps his most important.
Liverpool were soon handed a setback as Mats Hummels drew the home side level.
See Origi’s goal, below:
It was a game which marked Jurgen Klopp’s homecoming – click here to see 13 AMAZING photos from the evening.