'Job done' for Klopp
Paris, France - was disallowed for an Abraham handball.
The result means Ajax, Chelsea and Valencia are level on seven points atop Group H, with the Spaniards coming from behind to beat Lille 4-1.
Nigerian striker Victor Osimhen put Lille ahead at half-time, but Dani Parejo's penalty restored parity and Valencia then scored three times in the last eight minutes.
Adama Soumaoro's own goal was followed by a stunning Geoffrey Kondogbia strike and a Ferran Torres effort. Lille is eliminated.
Liverpool won 4-1 in Genk two weeks ago and looked on course for another comfortable victory against the Belgians when Georginio Wijnaldum gave it the lead at Anfield.
However, with manager Jurgen Klopp resting several players ahead of this weekend's clash with Manchester City, the reigning European champion was pegged back.
Tanzanian striker Mbwana Ally Samatta headed Genk level before the interval, and it took a fine strike by Alex OxladeChamberlain to win the game.
"The plan was to win the game and we did that, so job done," admitted Klopp.
Liverpool is top of Group E, a point above Napoli, which could have qualified for the last-16 with a win against Salzburg but was held to a 1-1 draw.
Haaland on target
Erling Braut Haaland's early penalty - the 19 year old's seventh Champions League goal this season - gave Salzburg the lead, before Hirving Lozano equalised.
In Germany, Inter looked to be heading for a second straight win against Dortmund as it raced into a 2-0 half-time lead with Lautaro Martinez and Matias Vecino scoring.
Yet Dortmund fought back in the second half to win the game as Achraf Hakimi grabbed a brace either side of a Julian Brandt goal.
It is a result that leaves Dortmund second in Group F, three points ahead of Inter and one behind Barcelona, which is still top despite a 0-0 draw at home to Slavia Prague.
Mats Hummels said a frank half-time team talk helped Borussia Dortmund come from two goals down to beat Inter.
"Inter were very clinical in the first half. They scored twice from two chances, unlike us," said Hummels, who was beaten for pace by Martinez for the opening goal.
"We left them little room to breathe after the break and were really strong in the second half. At the interval, we said that we needed to continue with the ball the way we had done so before, but we had to create more chances."
Messi denied
Lionel Messi almost scored one of his finest goals, hitting the woodwork at the end of an exhilarating run in the first half.
Barcelona had not failed to score in a home Champions League group game in seven years and this result followed a shock weekend defeat at Levante.
RB Leipzig tops Group G after goals by Diego Demme and Marcel Sabitzer gave the Germans a 2-0 win at Zenit Saint Petersburg.
Lyon is two points behind it in second following a 1-3 defeat of Benfica. Joachim Andersen and Bertrand Traore scored for Lyon either side of a goal from Memphis Depay, who has now netted in all four Champions League games this season. Haris Seferovic scored for Benfica.