Leon Bailey’s first-half goal gave the Belgians a deserved first-half lead but the Leesiders fought back valiantly, and came desperately close to scoring.
Cork boss John Caulfield will still fancy his chances of pulling off an upset at home in Turner’s Cross after this display, however.
City were unchanged for the third game in a row while Genk made one change from their predicted line-up with Greek striker Nicholas Karelis coming into the side for Neeskens Kebano, with the 24 year-old Congolese international and ex-PSG player starting on the bench.
Both teams lined-out 4-2-3-1 in front of 7,765 fans at the 25,000-capacity Luminus Stadium on a sunny yet humid evening in Flanders.
City went right at Genk from kick-off and Sean Maguire fired high and wide in the opening minute.
Seven minutes into the tie skipper Thomas Buffel got to the end line and his cross was headed just wide by Genk danger man Alejandro Pozuelo in what was an early warning shot from the home team.
Greek international Nikolas Karelis on the break fired wide of the far post and then Steven Beattie’s stinging drive forced Marco Bizot to a punched save after 12 minutes.
City won their first corner on 14 minutes and Kevin O’Connor’s ball was headed wide by Maguire.
Cork had made a solid start with 20 minutes gone before skipper Greg Bolger was lucky to escape a card that would have kept him out of the return for a tackle on Buffel on halfway but the aging Genk skipper made the most of it.
Cork had been solid and composed for the best part of half an hour before Genk hit the front when they punished an error between Maguire and right-back Michael McSweeney on the half way line.
Karelis picked up the loose ball and immediately played pacey Jamaican winger Leon Bailey in on goal and he scored with a low left footed drive and for the first time in this European adventure Cork found were themselves a goal down.
Minutes later, Bailey was in again around the back of the covering McSweeney, but McNulty was well placed to make the save this time.
City remained calm and patient in the second half and were close to an equaliser on 54 minutes when Bolger and Beattie combined down the right to set up Maguire but he scooped the ball over the bar.
Kevin O’Connor and Maguire again went close to that elusive away goal but Cork took encouragement from this spell of pressure coming up to the hour mark on a hot and sticky night in Genk.
McNulty saved Pozuelo’s free kick after Alan Bennett and Maguire were booked but they are still eligible to play in next week’s eagerly anticipated second leg that is sure to draw the biggest crowd of the season to the Curragh Road venue and that’s least this Cork City team deserve.
Genk (4-2-3-1) - Bizot; Walsh, Dewaest, Wouters, Uronen; Pozuelo, Ndidi; Buffel (capt), Karelis, Bailey; Samatta.
Kebano for Karelis (72 mins), Heynen for Pozuelo (82 mins)
Cork City (4-2-3-1) - McNulty; McSweeney, Bennett, Browne, O’Connor; Bolger (capt), G. Morrissey; Beattie, Buckley, Dooley; Maguire.
D. Morrissey for Beattie (82 mins), O’Sullivan for Maguire (86 mins)
Clayton Pisani (Malta)