Hannover, Bayer Leverkusen and Borussia Monchengladbach could not make it through to the next round while Stuttgart, who put their dismal domestic form to one side, progressed courtesy of goals by Arthur Boka and Christian Gentner.
The performance made it all seem fairly straightforward for the Bundesliga side, who arrived with question marks hovering over them after only ending a run of five straight league defeats by beating Hoffenheim 1-0 at the weekend, while a 1-1 draw in the first leg left this tie delicately poised.
Genk were the first to seriously threaten a goal when Glynor Plet's powerful shot from the edge of the area was deflected for a corner by Serdar Tasci in the 10th minute, but Stuttgart were otherwise strong early on.
Shinji Okazaki was denied a brilliant goal by Kalidou Koulibaly's block, before Vedad Ibisevic's curling effort sailed narrowly over.
Genk had sights of goal too but failed to worry Sven Ulreich, who held Benjamin De Ceulaer's first shot before watching another moments later drift wide.
Martin Harnik then blazed over at the other end before Koulibaly got in the block to keep out Ibrahima Traore's free-kick.
But it was from the resulting corner that the breakthrough came on the stroke of half-time, with Antonio Rudiger's outswinging ball finding its way to Arthur Boka to rifle home from the edge of the area.
Genk had a chance to level early in the second half, but while Julien Gorius got plenty of power on his header, it did not have the direction as it went wide of the left-hand post.
Instead, Stuttgart threatened a second with a fine effort from Traore bringing a good save from Laszlo Koteles before Ibisevic shot over when well placed.
The second finally came in the 58th minute, with Gentner finding the corner of the net after being teed up by William Jorgensen.
Ibisevic sought to kill it off entirely with a third moments later but could not find the target.
There was still almost half an hour to play, but few chances came for either side, with Stuttgart happy to shut up shop and start planning for the next round.