On a night of milestones, the Light Blues marked Allan McGregor's record-breaking 83rd European appearance for the club with their 150th win in continental competition to seal qualification with a game to spare.
It also mean boss Steven Gerrard - who was overseeing his 40th Europa League game in charge of Gers - has now masterminded progression to the group stages for the second year running and with it a much needed cash bonanza.
But it was far from plain sailing as Philippe Montanier's men gave the unbeaten Ibrox outfit their most testing 90 minutes of the season so far.
They twice led after Maxime Lestienne and Duje Cop struck either side of Connor Goldson's equaliser.
But the resolve that has taken the Light Blues all the way to December without a blemish on their record shone through again and they claimed the win they needed thanks to James Tavernier's penalty - the skipper's 15th goal of the season - and Scott Arfield's second-half winner.
Gerrard kept faith with the same line-up that blew the chance to seal qualification last week after throwing away a two-goal lead over Benfica.
But McGregor's special night did not get off to the start he was hoping for as he surpassed Barry Ferguson's appearance record.
The former Scotland number one had previously kept 37 European clean sheets but there was to be no shut-out this time as Standard netted the opener inside six minutes.
Laurent Jans' first-time ball took Tavernier out of the picture, while Goldson's hesitancy allowed Cop to fire a cross to the front post for Lestienne to turn home as Barisic arrived too late.
Rangers were looking nothing like the team which had strolled through their opening 23 games of the campaign, with both their passing and pressing off beat.
The Belgians were not helping Gerrard's team to find their rhythm as they exploited the huge spaces the hosts were leaving down their flanks every time Barisic and Tavernier bombed on.
Balogun was grateful to see Abdoul Fessal fire a wild effort wide after he was forced into a loose header by a long ball which threatened to drop over the Nigerian's shoulder.
But Rangers did eventually get a foothold, with signs of promise coming as Ryan Kent curled wide before Alfredo Morelos drove straight at Arnaud Bodart.
They may not have deserved it but they were level on 39 minutes as Goldson peeled off Merveille Bokadi to meet Barisic's corner, powering a fine header back across Bodart for the equaliser.
But Gers were caught sleeping almost immediately and fell behind again just a minute later. Glen Kamara failed to get out quickly enough to stop Collins Fai collecting a free-kick down the right and his cross was allowed to bounce all the way to the back post where Cop bundled home.
It was a brave finish from the Croatia winger, who suffered a sore one as he collided with the back post.
But the flurry of goals was not done there and Gers found themselves on terms again on the stroke of half-time.
Referee Bojan Pandzic appeared to point for a corner after a Kemar Roofe strike deflected off Lestienne on its way out of play - but consultation with his assistance alerted the Swedish official to the fact it had hit the opening goalscorer's hand and to the dismay of the visitors, a penalty was awarded.
Tavernier did not care about the protests, however, as he fired his ninth successful spot-kick of the season straight down the middle.
The Premiership leaders were not out of the woods just yet though and found themselves pinned back as the action resumed.
McGregor flapped at a corner but looked more assured as he blocked a Fessal attempt.
And having survived that period of pressure again, Gers grew in belief before snatching the precious lead on 63 minutes.
Kamara picked his moment to slide Kent in behind with a reverse pass. The winger could have flashed across the six-yard box for the marked Morelos but wisely chose to pull back for Arfield, who coolly slotted home the third.
Gers could have done with another to make the final stages a bit more comfortable but Bodart was in stubborn form, brilliantly denying Tavernier, Barisic, Goldson and Roofe in the final stages.
But there was no repeat of their Benfica lapse as Gers again extended their European campaign past the new year.
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