Victory saw the Belgian side move on to 11 points, meaning they qualify from Group G with a game to spare, but Videoton must now win their final game against Sporting Lisbon and hope Basle do not succeed against Genk.
Videoton have been in good form and they made all the early running, Adam Gyurcso soon involved with a shot that was blocked before firing over from Alvaro Brachi's cross.
However, it was Genk who took the lead in the 19th minute when Barda headed home Julien Gorius' corner from the right.
Gyurcso then put a shot wide from close range before supplying a cross for Felipe Oliviera, who headed over.
Gyorgy Sandor continued the Videoton pressure by firing wide and Nermanja Nikolic shot over as the hosts continued to find themselves in good positions, but it was the visitors who led at the break.
Sandor fired over as Videoton kept on probing, but, although they were enjoying by far the greater share of possession in attacking areas, they could not force Genk keeper Kristof Van Hout into any real action.
Istvan Kovacs and Nikoli both shot over, while Alvaro Brachi's free-kick was too high, and it was hard to see how Videoton were going to translate all their pressure into an equalising goal.
Indeed, Genk almost doubled their lead 13 minutes from time when Jelle Vossen drew a block from home keeper Mladen Bozovic.
Videoton appeared to run out of steam and Bozovic was twice called on to punch clear in injury time.