Goals from Jelle Vossen, Bennard Kumordzi and Benjamin De Ceulaer, following Andriy Yarmolenko's opener for Dynamo, saw Mario Been's Belgian side remain top of the group with 11 points ahead of their final group clash at FC Thun next month.
Rapid Vienna's 2-1 victory over Thun means the race for second spot is still on, with Dynamo currently second with seven points and the Austrian outfit a point further back. The two sides meet in Kiev in two weeks.
Genk enjoyed the majority of possession in the opening stages on Thursday night, but it was Oleh Blokhin's side that took the lead after nine minutes as they capitalised on the first real chance at the Cristal Arena.
Ukraine striker Yarmolenko thumped home a shot with his left foot from the right of the area as he found the back of the net for his seventh time this season.
Genk tried to pull a goal back as Julien Gorius had a chance to equalise two minutes later, but his effort from just outside the area sailed over the crossbar.
The leveller arrived in the 17th minute as Vossen netted from the penalty spot after Kumordzi was fouled by Yevhen Khacheridi.
The Belgium striker made no mistake as he stepped up and fired the ball high in the centre of the goal, beating Dynamo stopper Koval to make it 1-1.
The home side began to dominate and their pressure paid off as they took the lead eight minutes before the break.
Thomas Buffel provided a header from the edge of the area which Kumordzi pounced on and netted from close-range.
And three minutes later De Ceulaer scored their third from Gorius' corner, giving the hosts a 3-1 lead at half-time.
Both sides took a while to get going after the break, with Yarmolenko coming closest to pulling one back for the Ukrainian side, his weak shot floating over the bar.
De Ceulaer could had added his second as the game approached the hour mark, but Dynamo's Yevhen Khacheridi put in a great block to prevent his side slipping further behind.
And Khaleem Hyland was unlucky as Koval managed to keep out his 25-yard thunderbolt with 20 minutes to go as the home side pushed for a fourth.
The away side, who seemed more and more deflated as the match wore on, did not really come close in the second half and Miguel Veloso's weak effort in the closing minutes summed up their night.