The match was rearranged for Friday afternoon after the initial tie was postponed following three pitch inspections due to fog at the Mapei Stadium.
The game itself was a dead rubber as Genk had already qualified for the last 32 and Sassuolo had no mathematical chance of reaching the knockout rounds, but it was the hosts who did well to keep their opponents at bay in the first half.
Genk struggled to find a way through initially, with Leon Bailey having a handful of opportunities, one of which resulted in a shot from the edge of the box, but Sassuolo's defence stood firm.
Mbwana Samata had a decent opportunity to open the scoring when he latched onto a rebound, but he could only send the ball wide of the post.
At the other end, the hosts got a sniff at goal when Claud Adjapong met the end of a corner kick and directed a header towards the net, only to miss the target and send the ball over the crossbar.
The breakthrough came in the 58th minute when Samata teed up Bryan Heynen, who drilled the ball past the keeper from close range, and after taking the lead, confidence grew among the players.
Heynen tried to make it two when he let fly a low shot after getting on the end of a deep pass, but the goalkeeper was alert and managed to prevent the ball from nestling into the back of the net.
Luca Mazzitelli had an effort to equalise, only for his rebound shot from the edge of the box to clatter off the crossbar, and it was not long before Genk were celebrating a second goal.
Genk head into the knockout stage alongside Athletic Bilbao.