The Reds came into the game having lost their opening three fixtures in the competition, most recently last week against Rosenborg 3-0, but started the game in confident fashion.
Lloyd Jones found the net on 15 minutes with a powerful header that flew past keeper Jacob Storevik, shortly before Adam Morgan extended their lead with a clever finish to put Liverpool 2-0 up.
The visitors fought back well, with Martin Lundal scoring a brilliant 25-yard strike to keep them in the game. A well-timed second Adam Morgan goal just before the break meant the half-time score was 3-1 to the hosts.
The game was played in fine spirit, with both teams eager to impress with their attacking football. Liverpool looked the stronger, and grabbed a deserved fourth through Jerome Sinclair on the stroke of full-time to wrap the tie up.
The result keeps Liverpool in the hunt for qualification, with their next game at home to Borussia Dortmund later this month.