Liverpool are unbeaten domestically and six points ahead of City as they chase their first league title in 30 years.
Winaldum opened the scoring in the 14th minute.
Liverpool came up against Berge on Tuesday night, as he started in the middle of the park for Genk at Anfield. Despite 28 shots on goal and 71 per cent of possession, Liverpool struggled to really dominate and only scored two goals.
Liverpool will be looking to maintain their good run of form this evening when they take on KRC Genk in the Champions League.
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 the restart.
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The game's biggest moment was decided by its best player.
Captain Jordan Henderson, Fabinho and Georginio Wijnaldum have formed a solid midfield trio for Liverpool in recent months but Oxlade-Chamberlain's goalscoring threat and playmaking qualities will give manager Jurgen Klopp a selection headache.
But credit to Genk, who didn't lie down, even after taking their most risky player, Junya Ito, off and replacing him with Dieumerci Ndongala.
It was Genk who was pushing for a goal in the games final minutes though and Allison was forced to make a smart save after Casper de Norre lifted over a deft pass to Heyner, whose half-volley was pushed wide by the Brazilian.
"The most important thing; we won and nobody is injured".
Napoli was held to a 1-1 draw by Salzburg in the group's other game.