Ryan Kent's second-half finish restored Rangers' three-goal cushion in the last-16 tieRangers reached their first European quarter-final in 14 years after a resilient second-leg showing at Red Star Belgrade sealed a landmark Europa League aggregate victory.
Mirko Ivanic drilled in an early opener to give the Serbian champions hope at the hostile Rajko Mitic Stadium.
But Ryan Kent's deflected second-half finish ended the tie as a contest after Allan McGregor made several key saves.
Ben Nabouhane grabbed a late Red Star consolation from the spot.
Rangers were rocked for spells with the aggregate scoreline at 3-1, but yet again their veteran keeper was on hand to deliver another outstanding performance in his 99th European appearance for the Scottish champions, ensuring their advantage was not reduced further.
The Ibrox side will discover their last-eight opponents in Friday's draw, the first time they have reached this stage since their journey to the Uefa Cup final in 2008.
Prior to kick-off, only one team in Europa League history - Valencia against Basel - had overturned a deficit of three or more in the first leg of a knockout tie - and Rangers were in no mood to be the second victim.
In a cauldron of noise at Belgrade's 'Marakana', the Ibrox side were calm and composed in the early exchanges, with Alfredo Morelos first to test the goal with an ambitious strike from the right of the Red Star box.
But the hosts clicked into gear after 10 minutes and ordered Rangers to show a huge test of character when Ivanic drilled in an opener on the night.
Guelor Kanga delivered a short corner into the box and hesitant defending from the away side allowed the ball to bounce before the 28-year-old took one touch and hammered past McGregor.
Rangers' impressive early work quickly turned to panic as Red Star came close to adding a quickfire second when Ivanic struck across McGregor on the break, but the Rangers keeper's vital left hand tipped the goal-bound effort around the post.
Red Star boss Dejan Stankovic said his side would be "twice as strong" in the return leg, and Rangers were getting a taste of that as a raucous crowd roared on every home attack.
The visitors looked spooked, but the Serbian hosts' desperation for more goals provided space on the break for the Ibrox side to expose.
Morelos spurned a three-on-two opportunity when he failed to find Kent with a pass, and that was almost immediately punished when Ohi Omoijuanfo nodded a back-post header into the arms of McGregor straight up the other end.
Another opening for Morelos was dragged wide of the far post, with Red Star again seeing a chance fall their way in the aftermath.
The Rangers backline failed to deal with a long ball as Milan Pavkov was able to pick up the scraps, but the Red Star forward watched his finish trickle by the left-hand post when the forward ought to have found the net.
The Scottish champions have found themselves involved in basketball-like affairs in this season's knockout stage, but as the half progressed the game became stop-start, allowing Van Bronckhorst's men to take breath and slow the game down.
There was still time for McGregor to make a crucial first-half intervention when Cristiano Piccini's curling effort was tipped over by the 40-year-old - a crucial moment in the tie - and the Rangers stopper was again at full stretch to react to a Red Star corner early in the second period.
There was then a one-on-one opportunity for Omoijuanfo, who outmuscled Calvin Bassey but overhit a simple pass to Pavkov, who was lurking for a simple tap-in.
It was a sliding-doors moment for Red Star as Glen Kamara's pass in behind the home defence soon after saw Kent race clear and guide a deflected finish over Milan Borjan.
That goal sapped the energy out the home crowd, but their side continued to pepper the Rangers goal as Ivanic had an effort drag past the back post and a header parried to safety by McGregor in quick succession.
The resulting corner saw McGregor make a rare fumble from Kanga's long-range effort, but the keeper recovered to gather Nabouhane's rebounded effort which really should have burst the net.
Kemar Roofe, who came on for the injured Morelos, was denied a fifth for Rangers when the substitute forced Borjan down to his right.
But it would be Red Star who would have the last say when Kamara gave away a penalty for a step on the toe of Filippo Falco.
Nabouhane converted low to the left, sending McGregor the wrong way, but it was no more than a consolation as Rangers progressed on another memorable European night for this set of players.
Man of the match - Allan McGregor
The evergreen 40-year-old was absolutely crucial again for his side, making a string of stunning saves at vital times in the gameWhat did we learn?
Competition favourites Borussia Dortmund? Tick. Serbian champions Red Star? Tick. Who next?
Champions League calibre opposition in Barcelona, Atalanta and RB Leipzig potentially lie in wait for Van Bronckhorst's side - but would anyone fancy being paired with this Rangers side, who continue to shine on the European stage?
A two legged quarter-final adds more minutes and mileage to a season-defining April, but the Ibrox club must embrace a first last-eight venture in 14 years.
With Dortmund and Red Star side dispatched in empathic style, anyone with allegiances to Rangers deserves to dream.
What the manager said
Rangers manager Giovanni van Bronckhorst told BT Sport: "I'm very proud - it's a great achievement to reach the last eight. We knew it would be difficult. Our belief is only getting stronger.
"There are big teams left in the draw. The opponent will be stronger with each round. The result against Dortmund is one that the whole of Europe thinks is a great achievement."
What the stats say
Rangers have now won only one of their last six Uefa Europa League away games (D3 L2), while they have conceded in each of their last seven such games; excluding qualifiers, it's their longest such run in major European competition since September 1999 (run of 13).Since the start of last season, only Bayer Leverkusen (9) have scored more goals from set pieces (ex. penalties) in the Uefa Europa League than Red Star (8). All four of Ryan Kent's Uefa Europa League goals have come in the knockout stages. Since 2018-19, no Rangers player has scored more goals in the knockout stages than him (James Tavernier also 4). At 40 years and 45 days, Rangers' Allan McGregor is the oldest goalkeeper to make at least 11 saves in a Europa League game, while it's the most in the knockout stages of the competition since Copenhagen's Karl-Johan Johnsson against Man Utd in August 2020 (13).What's next?
Rangers turn their focus to reclaiming their Scottish Premiership title on Sunday when they travel to bottom side Dundee (12:00 GMT).
Player of the match
McGregorAllan McGregor
Red Star Belgrade
Squad number15Player nameDragovic
Squad number82Player nameBorjan
Squad number24Player namePiccini
Squad number8Player nameKanga
Squad number9Player namePavkov
Squad number10Player nameKatai
Squad number25Player nameErakovic
Squad number4Player nameIvanic
Squad number23Player nameRodic
Squad number31Player nameBen Nabouhane
Squad number35Player nameSanogo
Squad number17Player nameMotika
Squad number11Player nameFalco
Squad number99Player nameOmoijuanfo
Squad number2Player nameGajic
Rangers
Squad number1Player nameMcGregor
Squad number4Player nameLundstram
Squad number14Player nameKent
Squad number26Player nameBalogun
Squad number2Player nameTavernier
Squad number8Player nameJack
Squad number6Player nameGoldson
Squad number3Player nameBassey
Squad number18Player nameKamara
Squad number17Player nameAyodele-Aribo
Squad number20Player nameMorelos
Squad number25Player nameRoofe
Squad number37Player nameArfield
Squad number19Player nameSands
Squad number31Player nameBarisic
Squad number23Player nameWright
Line-ups
Red Star Belgrade
Formation 4-1-2-1-2
82Borjan
24Piccini25Erakovic15Dragovic23Rodic
35Sanogo
8Kanga4Ivanic
10Katai
9Pavkov99Omoijuanfo
82BorjanBooked at 90mins24PicciniSubstituted forGajicat 57'minutes25Erakovic15DragovicBooked at 70mins23RodicSubstituted forFalcoat 72'minutes35Sanogo8Kanga4IvanicSubstituted forMotikaat 72'minutes10KataiBooked at 83mins9PavkovBooked at 90mins99OmoijuanfoSubstituted forBen Nabouhaneat 63'minutesSubstitutes
1Popovic2Gajic6Pankov7Krsticic11Falco17Motika31Ben Nabouhane38Stankovic49Radulovic55Srnic77GobeljicRangers
Formation 4-2-3-1
1McGregor
2Tavernier6Goldson26Balogun3Bassey
4Lundstram8Jack
17Ayodele-Aribo18Kamara14Kent
20Morelos
1McGregor2Tavernier6Goldson26Balogun3Bassey4LundstramSubstituted forBarisicat 81'minutes8JackSubstituted forSandsat 69'minutes17Ayodele-AriboSubstituted forArfieldat 68'minutes18KamaraBooked at 90mins14KentSubstituted forWrightat 90'minutes20MorelosSubstituted forRoofeat 80'minutesSubstitutes
9Diallo16Ramsey19Sands23Wright25Roofe28McCrorie30Sakala31Barisic33McLaughlin37Arfield43King51LowryLive Text
Match ends, Red Star Belgrade 2, Rangers 1.
Milan Borjan (Red Star Belgrade) is shown the yellow card.
Second Half ends, Red Star Belgrade 2, Rangers 1.
Hand ball by Kemar Roofe (Rangers).
Offside, Red Star Belgrade. Aleksandar Dragovic tries a through ball, but Milan Pavkov is caught offside.
Milan Pavkov (Red Star Belgrade) is shown the yellow card for a bad foul.
Foul by Milan Pavkov (Red Star Belgrade).
Connor Goldson (Rangers) wins a free kick in the defensive half.
Goal! Red Star Belgrade 2, Rangers 1. El Fardou Ben Nabouhane (Red Star Belgrade) converts the penalty with a left footed shot to the bottom left corner.
Glen Kamara (Rangers) is shown the yellow card for a bad foul.
Penalty Red Star Belgrade. Filippo Falco draws a foul in the penalty area.
Penalty conceded by Glen Kamara (Rangers) after a foul in the penalty area.
Attempt blocked. Kemar Roofe (Rangers) right footed shot from the centre of the box is blocked. Assisted by Scott Arfield.
Substitution, Rangers. Scott Wright replaces Ryan Kent.
Aleksandar Katai (Red Star Belgrade) wins a free kick on the right wing.
Foul by Ryan Kent (Rangers).
Strahinja Erakovic (Red Star Belgrade) wins a free kick in the defensive half.
Foul by Kemar Roofe (Rangers).
Foul by Milan Gajic (Red Star Belgrade).
Glen Kamara (Rangers) wins a free kick in the defensive half.
