Former Tema Youth winger Joseph Paintsil, 20, and ex-Inter Allies centre-back Joseph Aidoo, 23, both found the back of the net for the home side, who claimed a 4-0 triumph at Luminus Arena.
The result was enough to seal Blauw-Wit's place in the next round of the competition as Group I winners.
It took Genk just two minutes to break the deadlock as Sander Berg set up Zinho Gano for the opener.
Paintsil then made it 2-0 three minutes later, having been assisted by Alejandro Pozuelo.
In the 64th minute, Berg added his name to the scorers before former Ghana U-20 captain Aidoo sealed the win with a 67th-minute strike.
The Ghanaians lasted for the entire duration of the game.
While it was Aidoo's first Europa League goal in five career appearances in the competition, it was Paintsil's second strike of the championship, having earlier netted in last month's 2-2 draw with Swedish side Malmo.
The pair will hope to continue their good form when Genk host KV Oostende in the Belgian topflight on Sunday.