This victory saw the Reds finish third in the league standings with 18 points from eight matches.
Meanwhile, Qarabag, despite suffering a heavy defeat, still has the right to advance to the playoff round after finishing 22nd with 10 points, as reported on the official UEFA website.
Liverpool dominated from the start. However, they were forced to make a quick substitution after Jeremie Frimpong was substituted off in the third minute with an injury.
The hosts opened the scoring in the 15th minute. Alexis Mac Allister got his name on the scoresheet after tapping in Dominik Szoboszlai's corner kick at the far post unmarked.
