Daniel Sturridge opened the scoring after 10 minutes and Dejan Lovren doubled their advantage three minutes later as Brendan Rodgers’ side took control early on.
Philippe Coutinho added a third in the 49th minute and Jordan Henderson completed the scoring just after the hour mark.
Liverpool made a habit of starting strongly in the Premier League last term and they began quickly as Sturridge, Coutinho and Raheem Sterling all caught the eye.
The breakthrough came when Lovren’s ball into midfield was quickly played on by a clever Coutinho pass to release Sturridge, and he coolly finished into the bottom corner.
Lovren, one of three summer signings in the starting XI, headed in a corner three minutes later and helped Liverpool hold their lead until half-time with a solid defensive performance as Dortmund enjoyed more possession.
Liverpool increased the tempo again at the start of the second period and made it 3-0 as Sterling seized on a loose pass from Matthias Ginter and fed Coutinho, whose quick feet got him away from a couple of defenders before he drilled in a low shot.
Coutinho played his part in another fine move to create the fourth, although it looked as though the ball may just have gone out of play before Sturridge was able to cross for Henderson to slide home from close range.
The closing stages were disrupted by a host of substitutions on both sides but Liverpool kept their focus to keep a clean sheet and set them up perfectly for next weekend’s league opener against Southampton.