Thanks to Rapid Vienna's victory against Dinamo Zagreb earlier on Thursday evening, David Moyes' men are now six points clear at the top of Group H.
Without danger man Michail Antonio up front, the Hammers actually looked rather toothless up front as the visitors started brightly.
Theo Bongonda even had the ball in the back of the net after a great break from Junya Ito down the right hand side, only for it to be ruled offside.
It seemed to spark the home side into life and, roared on by a partisan crowd at the London Stadium, they took the lead when Craig Dawson nodded home Aaron Cresswell's corner on the brink of half time.
Despite the lack of a natural target man, West Ham were dominating the ball and Declan Rice and Tomas Soucek quickly began to control the midfield areas.
The lead was doubled when Angelo Preciado needlessly brought down Nikola Vlasic, with Cresswell again turning provider as his free kick was nodded in via the bar by Issa Diop.
Temperatures in east London had slowly begun to edge towards zero, but West Ham were now fired up and quickly snatched the game from Genk when Jarrod Bowen collected a quick turnover ball and drove at the defence before lashing home past the 19-year Maarten Vandervoort in goal.
A flurry of changes somewhat slowed the game to an almost pedestrian pace, yet this victory was the perfect warm up for a London derby against rivals Tottenham on Sunday and the reverse fixture in the first week of November.