Alfredo Morelos, putting his League Cup Final despair firmly behind him, set Steven Gerrard’s men on their way with his 14th European goal of the campaign in a dominant first half against Swiss champions Young Boys.
Rangers were on course to top the group at that stage but had to endure a tense finale after Borna Barisic’s late own goal gave Young Boys a sniff of the victory they needed to qualify for the knockout phase.
Gerrard’s men saw it out, despite Ryan Jack’s dismissal for two bookable offences, but had to settle for second place in Group G which means they will be unseeded in next Monday’s round of 32 draw.
Rangers looked determined from the very start not to leave themselves as hostages to the myriad permutations in a group where all four teams began the evening with their hopes of qualification still alive.
There was even a scenario in which Gerrard’s men could still progress with a defeat in the event that Feyenoord won in Porto.
But while scoreflashes filtered through regularly from that fixture, Gerrard’s men were solely focused on making it under their own steam.
There was no sign of any negative after effects from Sunday’s League Cup Final disappointment as Rangers set about imposing themselves on Young Boys with feverish intensity.
Morelos caught his first sight of goal after just four minutes but was unable to execute his attempt to meet Joe Aribo’s cross from the right with a reverse flick at the near post, the ball flashing across the six yard box.
Rangers continued to probe with pace and purpose, restricting the visitors to very occasional forays in the direction of Allan McGregor’s goal.
Scott Arfield saw a shot deflected wide off Christopher Pereira as the hosts began to carve out a series of chances and Morelos might have done better than drill a shot straight at Young Boys goalkeeper David von Ballmoos after latching onto Aribo’s fine through ball.
The striker then had a claim for a penalty waved away by German referee Felix Brych after going down under what certainly appeared to be a clumsy challenge from Frederik Sorensen.
But Morelos’ scowl was replaced by a joyful grin when he put Rangers ahead on the half hour mark. The goal was a comedy of errors for the visitors’ defence, beginning with Nicolas Burgy’s slack pass which gifted possession to Ryan Kent.
Even then, Kent’s through ball towards Morelos was not the sharpest and should have been cut out by Sorensen. But the big central defender made a mess of it, his uncertainty seized upon by Morelos who raced clear and coolly drove the ball beyond Von Ballmoos.
The Rangers players sprinted en masse to join Morelos in his celebrations, recognising the significance of the moment for the striker who endured such an agonising afternoon at Hampden four days earlier.
Rangers were in firm control of proceedings and should have added to their lead before the interval, passing up several decent opportunities.
Kent’s clever flick found Arfield on the right of the Young Boys penalty area but instead of cutting the ball back to Aribo, he attempted a shot from a difficult angle which Von Ballmoos was able to divert wide.
The lively Aribo was causing real anxiety in the visitors’ defence with his trickery and directness and he came close twice, first heading just wide from a superb Borna Barisic cross and then screwing a shot off target after being picked out by Morelos.
Young Boys had offered next to nothing as an attacking force but there was a reminder for Rangers on the stroke of half-time when Christian Fassnacht, scorer of the stoppage time winner when the teams met in Bern earlier in the group, headed narrowly over from Ulisses Garcia’s cross.
Rangers resumed on the front foot after the break and Morelos had the chance to give them the comfort of a second goal in the 48th minute when he was sent scampering down the right but after forcing his way into the penalty area, his low shot was kept out by Von Ballmoos.
To the increasing consternation of Gerrard on the touchline, however, Rangers struggled to maintain the attacking momentum they had enjoyed in the first half.
Young Boys began to secure a greater share of possession as they played with a greater tempo in their efforts to turn the situation around.
Nerves began to creep into Rangers’ play and when Glen Kamara gave the ball away cheaply in a dangerous position, Jack was left with little option but to commit the foul on Michel Aebischer which earned his first booking.
Rangers suddenly looked vulnerable and it needed a tremendous save from McGregor to deny Fassnacht an equaliser, the veteran ‘keeper touching his header over.
Young Boys threatened again when Barisic had to time his tackle perfectly to halt Aebischer inside the penalty area.
Van Ballmoos stood tall to make another smart stop from Morelos in what was now a more rare burst forward from the tiring hosts as the clock ticked down.
Time didn’t pass quickly enough for Rangers’ liking and they found themselves teetering on the edge of calamity when Young Boys equalised in the 89th minute, Barisic turning the ball into his own goal as he attempted to clear a shot from substitute Felix Mambimbi.
The excruciating closing minutes saw Jack collect his second yellow card but Rangers held on for the point that was sufficient to take them through.