The visitors ran roughshod in the first half to lead 4-1 by half-time at the Ghelamco Arena and withstood a second-half fightback in which Kalifa Coulibaly reduced the deficit and Jeremy Perbet missed a penalty.
Only one place and two points separates the teams in the Belgian First Division A and that initially showed as Ruslan Malinovskyi's fine opener for Genk was cancelled out by Samuel Kalu in a well-balanced opening 30 minutes.
But Genk took complete control of the tie as Omar Colley, Mbwana Samatta and Jere Uronen scored before half-time, with the quality of their set-pieces and speed on the attack proving too much for Gent.
The home side had overcome the odds to knock out highly fancied Tottenham in the previous round and even this considerable deficit seemed somewhat surmountable when Coulibaly pulled a goal back in the second half.
However, Mat Ryan's save from Perbet's spot-kick killed their momentum and Samatta's second after 72 minutes restored a three-goal lead for Genk heading into the return leg, while Gent's misery was compounded by Anderson Esiti's red card six minutes from time.
Gent should have led in the third minute, but Perbet somehow smashed the rebound against the crossbar inside the six-yard box after Ryan had saved Kenny Saief's low strike.
Ryan made another stop from Saief's 20-yard effort, but Genk quickly established a threat on the break and took the lead in spectacular fashion in the 21st minute when Malinovskyi curled a delightful free-kick in off Lovre Kalinic's left-hand post.
Gent levelled six minutes later when the lively Saief saw his teasing centre slice off the crossbar via Jakub Brabec and Kalu smashed the dropping ball into the net off Ryan from a tight angle.
Back came Genk and Jean-Paul Boetius shot straight at Kalinic, before Colley restored the lead by meeting Malinovskyi's corner - missed by the flapping the goalkeeper - with a firm header.
Malinovskyi's deliveries continued to cause problems and Samatta and Brabec missed further chances, before Kalinic made a smart parry from Siebe Schrijvers' drive.
And Genk took firm control with two goals in the last four minutes of the half.
Samatta sprung the offside trap to control Boetius' pass and smash his shot beyond Kalinic, who was then beaten by Uronen as Pozuelo prompted another ruthless move.
Gent responded after half-time, though, with Saief again central to the attack as he crossed for Coulibaly to nod past Ryan.
It looked as though Genk's lead would be cut further when Malinovskyi tangled with Kalu to concede a penalty with just over half an hour remaining, but Ryan brilliantly denied Perbet from 12 yards.
Samatta instead ensured the visitors would return home with considerable breathing space as he turned Thomas Buffel's cross into the net for a fifth.
And things went from bad to worse for Gent as Anderson Esiti, booked in the build-up to the first goal, earned a second yellow for a trip on Schrijvers and will now miss what appears an impossible rescue mission in the return leg.