Pione Sisto's strike was cancelled out by Leandro Trossard but Celta Vigo who advanced to the Europa League semi-finals at Genk's expense.
Celta Vigo advanced to the semi-finals of a major UEFA competition for the first time following a 1-1 draw against Genk in the second leg of their Europa League quarter-final at Luminus Arena.
A 3-2 victory in the first fixture at Balaidos proved key for Eduardo Berizzo's side, who had to withstand late pressure after Leandro Trossard cancelled out Pione Sisto's second-half opener.
The tenacious Sisto gave Celta a two-goal aggregate cushion when he created something out of nothing in the 63rd minute, but Genk hit back in less than four minutes through a delightful finish from energetic winger Trossard.
Genk had struggled to trouble Sergio Alvarez in the Celta net up until that point and failed to do so again despite controlling possession after the introduction of striker Siebe Schrijvers and winger Jean-Paul Boetius in the final 20 minutes.
Claudio Beauvue - a first-half replacement for John Guidetti, who was forced off through injury - could have put the tie to bed much earlier but the Celta forward was twice denied by goalkeeper Mat Ryan.
The Belgian side ended up falling just short, unable to find the additional goal that would have put them and not Berizzo's men into the hat for the final four.
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Genk created a chance inside five minutes when Trossard's left-wing cross found Mbwana Samatta in the box, the striker looping a header onto the roof of the net.
Celta responded quickly and Gustavo Cabral poked agonisingly wide when captain Thomas Buffel inadvertently deflected a free-kick to his feet inside the six-yard box.
Jakub Brabec gifted the visitors another opportunity in the 16th minute when his poor attempt at a clearance fell to Sisto. The Denmark international shifted the ball onto his right foot and curled a lovely 20-yard shot narrowly past the upright.
Celta were unable to turn their control of possession into chances and they lost Guidetti to injury before half-time.
Beauvue replaced the striker and within two minutes forced Ryan into a great save down to his left with an acrobatic effort from Hugo Mallo's delivery.
Trossard bent an effort wide as Genk mounted a positive start to the second period, although Beauvue provided a reminder of the threat Celta pose on the break when only a strong save from Ryan stopped him firing home from Iago Aspas' fine through ball.
Celta did break through just after the hour-mark, though, when Sisto caught Timothy Castagne in possession and raced forward before slamming a powerful, swerving drive beyond Ryan.
However, Genk equalised quickly when Trossard dispossessed a hesitant Cabral on the edge of the box and curled a fine finish into the bottom-right corner.
Albert Stuivenberg replaced Buffel and Ruslan Malinovskiy with Schrijvers and Boetius in the 72nd minute, but a wayward effort from the latter was all Genk could muster before the final whistle.
Frustrations boiled over late on when Pablo Hernandez kicked the ball away as substitute Sebastian Dewaest tried to take a quick throw-in, the pair booked as the Belgian side's European adventure came to a close.