Russell Martin’s side were forced to play with a numerical disadvantage for over 50 minutes when Mohamed Diomande was dismissed shortly before the half-time interval.
Indeed, the decision was sandwiched between a penalty decision which Rangers were denied when James Tavernier headed the ball onto the arm of Zakaria El Ouahdi and a spot-kick awarded to the visitors down the opposite end which Jack Butland thwarted.
However, the Belgian outfit made their strength in numbers tell in the second period when Hyeongyu Oh provided the exclamation point on a Genk breakaway to condemn the Gers to defeat on matchday one.
The Gers boss named just the solitary change from the side which defeated Hibernian on Saturday evening, rewarding summer signing Youssef Chermiti with his first start for the club.
Rangers signalled their intent to supply the former Everton forward in the opening exchanges with a sequence of early deliveries from Jayden Meghoma, the first of which was cleared only as far as James Tavernier who saw his lay-off skied over the top by Mikey Moore.
The on-loan Spurs wide men appeared on a one-man crusade to find an early opener for the hosts as, just moments later, he strode onto a short clearance at the edge of the penalty area and planted a strike into the ground and wide of the far post.
The home side ought to have got their noses in front just past the quarter of an hour mark but for a gravity-defying goalline clearance from Bryan Heynen. It was John Souttar in blue who met Tavernier’s curling free-kick delivery, nodding his header back across goal before he was denied by a matter of inches.
The near-miss seemed to rally the visitors who went down the opposite end and contrived to spurn a glorious opportunity when El Ouahdi drilled a low delivery towards Oh who ballooned over from close-range.
Patrik Hrosovsky was next to go close for the Belgian side when he shimmied beyond Nico Raskin inside the penalty area and dug out a curling effort which connected with the outside of Jack Butland’s far post.
As if to underline their threat going forward, a sweeping move down the left-hand side engineered space for El Ouahdi to centre in search of Oh. Fortunately for Rangers, Derek Cornelius did just enough to knock the Korean forward out of his stride.
El Ouahdi was at the centre of a contentious refereeing decision moments later when Tavernier rose highest from a deep cross at the far post to head against the outstretched arm of the Genk wing-back.
Although referee Matej Jug was advised to take a trip to the pitchside monitor – normally an indication of a decision being overturned – he subsequently called both players over and signalled that he had spotted an apparent push from Tavernier in the act of contesting a header.
The controversy then continued into the latter stages of the opening 45 minutes as the Gers were reduced to ten men when Diomande was shown a straight red card for a dangerous foul on El Ouahdi in midfield.
It left the Gers with an uphill battle, which never got any easier when the visitors were awarded a spot-kick upon a further VAR review after Yaimar Medina had darted into space in the penalty area and went down under minimal contact from Tavernier.
Ibrox couldn’t quite the believe the side’s misfortune, but they were soon showing their appreciation for Jack Butland who, as he so often does, sprung heroically to thwart Oh from 12 yards.
The sound of the referee’s half-time whistle provided a moment to pause following a frenetic conclusion to the opening period.
Opportunity then knocked for the ten-man hosts when another wicked Meghoma delivery was cleared only as far as Thelo Aasgaard, but the Norwegian international was guilty of snatching at his finish which sailed off target.
A stramash down in the Gers box then almost allowed Genk to steal a march in the scoreline, although Kayembe was guilty himself of being too eager in slashing his effort wide from a tight angle.
The Rangers backline raised their hands in an appeal for the offside flag to be raised moments later when Hrosovsky broke through the Gers rearguard, but the far side linesman was unmoved and it was Oh who failed to provide the finishing touch from close-range.
However, the Belgian visitors capitalised on their numerical advantage inside ten minutes of the second period when Oh sprung the offside trap on this occasion before steadying himself and lashing a left-footed finish beyond the diving Butland.
The home side were desperate to remedy the situation despite being shorthanded; Djeidi Gassama jinking inside from the left-hand side in trademark fashion and curling just wide of the far post.
Genk were reeling away in celebration with 21 minutes remaining as they thought they had doubled their advantage when Oh tapped home from a Hrosovsky pull-back. Replays, however, showed the Slovakian midfielder timing his run on the early side and VAR advised the referee to overturn his decision.
Still, Rangers' endeavour could hardly be faulted and they almost secured a point with two minutes remaining of normal time when the ball dropped invitingly to substitute Connor Barron at the edge of the penalty area following promising wing play from Gassama, but the midfielder's goalbound effort was heroically headed to safety by Matte Smets.
Three minutes of additional time were signalled by the fourth official, which proved insufficient in Rangers' attempts to find a leveller as time ran out on the hosts.
RANGERS: Butland, Tavernier, Souttar, Cornelius (Rothwell, 78), Meghoma, Diomande, Raskin, Aasgaard (Barron, 78), Moore (Antman, 45), Gassama, Chermiti (Miovski, 78)
Subs not used: Kelly, Wright, Djiga, Gentles, Danilo, Rice, Curtis, McCallion
GENK: Van Crombrugge, El Ouahdi, Smets, Sadick, Kayembe, Medina (Adediji-Sternberg, 63), Heynen, Bangoura (Nkuba, 78), Hrosovsky (Karetsas, 90), Steuckers (Sattleberger, 78), Oh (Erabi, 78)
Subs not used: Mounganga, J. Ito, Bibout, Sattlberger, Mirisola, Yokoyama, Palacios