With Manchester City's visit on Sunday looming large over proceedings there was a feeling this was a game which just had to be got out of the way with the minimum of fuss and disruption.
The home side took the lead in the 14th minute with a close-range effort from Wijnaldum after James Milner's low cross from the left bounced off Sebastien Dewaest and fell to the Dutchman who scooped home.
Several clubs have been monitoring him and he grabbed further headlines when he scored against Liverpool in Genk's 2-1 defeat at Anfield on Tuesday night.
Jurgen Klopp and his opposite number Felice Mazzu came out for the second half unchanged from the first spell.
Genk nearly went one better and took the lead when Bryan Heynen cut inside but he pulled his effort wide of the right-hand post.
The game's biggest moment was decided by its best player.
That goal lit a fire under the collective Liverpool stomachs and they went looking for the elusive third goal - one that could potentially kill the game off. Their football became more fluid and expansive and, at times, it was deserving of a goal.
Napoli visit Anfield on November 27 with Liverpool hoping to guarantee qualification for the last 16 before their final group game at Salzburg on December 10.