Julien Gorius and Jelle Vossen struck either side of the hour mark, and although Thun scored late on through Josef Martinez, there was no way back.
The Belgian side lead the group by three points, with Thun second on three points after Rapid Vienna and Dynamo Kiev drew in the night's other game in the pool.
Fabien Camus' early free-kick for Genk was saved before Martinez threatened for the Swiss side but found home goalkeeper Laszlo Koteles equal to the task.
Koteles' opposite number Guillaume Faivre made his second save to keep out Benji de Ceulaer's blast before Vossen headed Camus' corner wide.
Martinez shot wide but Genk were soon back on the attack, Faivre tipping a Camus drive round the post and Bennard Kumordzi off target from the resulting corner.
It took a good save from Koteles to keep them on terms at the interval, though, the Hungarian tipping Martinez's close-range header behind for a corner.
Kara Mbodji's header early in the second half was saved by Faivre but the opener was not long in coming for Genk.
In the 55th minute, Camus teed up Gorius 20 yards out and the midfielder fired the ball into the far top corner.
Vossen wasted little time in making it 2-0 in the 63rd minute, sweeping home Anele Ngcongca's cross from six yards.
Buffel's curler was saved by Faivre but Thun had not given up hope and substitute Christian Schneuwly's left-foot drive forced a superb save from Koteles.
They got one goal back in injury time when Benjamin Luthi cut the ball back for Martinez to fire home, but the hosts held on.