Liverpool manager Jurgen Klopp admitted some wasteful finishing almost cost the Champions League holders before Alex Oxlade-Chamberlain's goal against Genk took them to the brink of qualification to the knockout stages.
Oxlade-Chamberlain struck the winner with a neat turn and finish seven minutes after the break to put Liverpool 2-1 ahead after a bullet header from Genk's Mbwana Samatta had cancelled out Georginio Wijnaldum's opener.
But it was not as comfortable as the 4-1 win in Belgium last time out thanks to some poor finishing that allowed bottom side Genk, who have been eliminated, to get back in the game and almost level right at the end.
"We didn't finish our situations as we could have done. We had really big chances that we usually use but we don't do that. That keeps the game open," said Klopp.
"If you only score one, and they score one, then it's a lot of effort. The game starts new in the second half, pretty much. But the plan was to win the game and we did that, so job done."
The win leaves Klopp's side a point ahead of Napoli, who could only draw 1-1 with third-placed Salzburg, beforethe meeting between the pair at Anfield later this month.
Liverpool are also five points ahead of the Austrians and will qualify with a match to spare if they see off Carlo Ancelotti's off-form side.
They will be favourites against the Italians, who are also stuttering in Serie A thanks to a run of only one win in five league matches, as the Reds have a formidable record in Europe that has them unbeaten on home soil since losing to Real Madrid five years ago.
England international Oxlade-Chamberlain's winner came after his brace at Genk and an impressive performance as Klopp started with Roberto Firmino and Sadio Mane on the bench before the weekend's big clash with Premier League title rivals Manchester City.
Liverpool are unbeaten domestically and six points ahead of City as they chase their first league title in 30 years.
"It's a different competition. We are in the best possible shape but we have to recover, and then we will prepare for City," Klopp said.
Wijnaldum opened the scoring amid an onslaught in the opening moments from the Reds when Genk failed to clear James Milner's cross and he cleverly flicked past Gaetan Coucke.
Liverpool had good chances to double their lead through Mohamed Salah and Naby Keita before Samatta silenced the home crowd with a brilliant near-post header from Bryan Heynen's corner.
The leveller was no less than the Belgians deserved for a spirited effort in the later stages of the first half, but they were a goal down again soon after the restart.
The lively Salah found Oxlade-Chamberlain with some neat footwork and the 26-year-old midfielder turned sharply before lashing a left-footed shot into the bottom corner at the Kop end.
Genk didn't give up and Alisson had to be at his best to stop Heynen with 10 minutes left, but the hosts managed to stave off the fightback and make sure of an important three points.
