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Rangers will play at European football's top table for the first time in more than a decade after stunning PSV Eindhoven to reach the Champions League group stage.
The decisive moment of an absorbing tie finally came on the hour, when Malik Tillman intercepted a PSV pass out from defence and squared for Antonio Colak to find an empty net from six yards.
The Philips Stadion went almost silent and the home side could find no response in the final half hour despite a flurry of chances.
Rangers can now look forward to drawing some of the continent's biggest names in Thursday's draw, where they join rivals Celtic in pot four as the pair play in the group stage in the same season for the first time since 2007/08.
Also vital will be the minimum £25m windfall which will now come their way as the Ibrox side complete the turnaround from playing in Scotland's third division 10 years ago to the Champions League.
The feat was achieved with a huge amount of resilience as PSV threatened throughout, and also amid the controversy surrounding striker Alfredo Morelos, who was left at home due to concerns about his attitude and fitness.
Instead it was the man who has started in his stead all season, Colak, who was in the right place at the crucial moment to score his fifth goal in eight games after brilliant awareness from Tillman to read and shut down goalkeeper Walter Benitez's pass.
The inevitable response from PSV came as Philip Max shot wide, and goalkeeper Jon McLaughlin denied their star man Cody Gakpo when through on goal, and those were just the opportunities which came after Rangers' struck.
There were others, including a free header from Ibrahim Sangare and a shot from close-range from Luuk De Jong fired straight at McLaughlin, but ultimately there was no way through.
Rangers showed immense character to hang on and also had their own strong spells, with Tom Lawrence unlucky not to score with a fantastic curling effort which cannoned back off the bar.
But it was their European muscle memory which got Giovanni van Bronckhorst's team over the line, as they again proved a smart, skilful and gutsy team on the big stage, traits which characterised their run to last season's Europa League final.
Now, the club and its fans can look forward to testing themselves on the biggest stage.
Man of the match - James Sands
Triumph in tough circumstances - analysis
Rangers have impressed regularly in Europe in the last four seasons, and this performance underlines the belief and confidence in the group as they triumphed despite trying circumstances.
Van Bronckhorst made a huge call to leave out Morelos and travel with just one recognised striker in Colak, and their preparations were disrupted further before kick-of when their bus was held up by PSV fans. Then there was the fact their away record in Europe read just one win in 10.
But away from Ibrox and in a rowdy arena, they still produced the goods. It wasn't the swashbuckling football they showed on their run to Seville last season, but they were disciplined, rode their luck, and delivered big moments when it mattered.
Tillman's reading of the game was crucial, and McLaughlin's brilliant save from Gakpo kept them ahead. With Celtic already assured of their place in the group stage, it was vitally important for the club financially to keep pace and qualify.
The manager has to take huge credit for his influence on the team, having now guided them to six wins from six in two-legged European knockout ties. His calm authority and tactical nous have stood out particularly in cup competitions.
Almost exactly 10 years ago Rangers were held to a draw by Berwick Rangers in the third division, this caps the journey back. The league title two seasons ago was crucial, but now they can truly say they have returned to the top level.
What's next?
Ross County are the visitors to Ibrox in the Scottish Premiership on Saturday (15:00 BST), but before that they can enjoy Thursday's group stage draw, which takes place at 17:00.
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PSV Eindhoven
Squad number1Player nameBenítez
Squad number3Player nameTeze
Squad number5Player nameAndré Ramalho
Squad number4Player nameObispo
Squad number31Player nameMax
Squad number15Player nameGutiérrez
Squad number6Player nameSangaré
Squad number28Player nameSaibari
Squad number23Player nameVeerman
Squad number11Player nameGakpo
Squad number9Player namede Jong
Squad number7Player nameSimons
Squad number8Player namevan Ginkel
Squad number20Player nameTil
Squad number25Player nameCarlos Vinícius
Squad number29Player nameMwene
Rangers
Squad number33Player nameMcLaughlin
Squad number2Player nameTavernier
Squad number6Player nameGoldson
Squad number19Player nameSands
Squad number31Player nameBarisic
Squad number4Player nameLundstram
Squad number18Player nameKamara
Squad number11Player nameLawrence
Squad number71Player nameTillman
Squad number14Player nameKent
Squad number9Player nameColak
Squad number23Player nameWright
Squad number30Player nameSakala
Squad number37Player nameArfield
Line-ups
PSV Eindhoven
Formation 4-2-3-1
- 1Benítez
- 3Teze
- 5Ramalho SilvaBooked at 27minsSubstituted forMweneat 62'minutesBooked at 68mins
- 4ObispoBooked at 84mins
- 31MaxSubstituted forvan Ginkelat 85'minutesBooked at 88mins
- 15GutiérrezSubstituted forTilat 62'minutes
- 6Sangaré
- 28SaibariSubstituted forAlves Moraisat 76'minutes
- 23Veerman
- 11Gakpo
- 9de JongSubstituted forSimonsat 45'minutesBooked at 90mins
Substitutes
- 2Hoever
- 7Simons
- 8van Ginkel
- 16Drommel
- 20Til
- 22Branthwaite
- 24Waterman
- 25Alves Morais
- 26Luckassen
- 27Bakayoko
- 29Mwene
- 33Moreira de Oliveira
Rangers
Formation 4-2-3-1
- 33McLaughlin
- 2Tavernier
- 6Goldson
- 19Sands
- 31BarisicBooked at 72mins
- 4LundstramBooked at 64mins
- 18KamaraSubstituted forArfieldat 73'minutes
- 11LawrenceSubstituted forWrightat 73'minutes
- 71Tillman
- 14KentBooked at 66mins
- 9ColakSubstituted forSakalaat 90+2'minutes
Substitutes
- 1McGregor
- 3Yilmaz
- 8Jack
- 10Davis
- 17Matondo
- 23Wright
- 28McCrorie
- 30Sakala
- 37Arfield
- 38King
- 44Devine
- 69Ure
Live Text
Match ends, PSV Eindhoven 0, Rangers 1.
Second Half ends, PSV Eindhoven 0, Rangers 1.
Xavi Simons (PSV Eindhoven) is shown the yellow card for a bad foul.
Foul by Xavi Simons (PSV Eindhoven).
Ryan Kent (Rangers) wins a free kick in the attacking half.
Attempt missed. Marco van Ginkel (PSV Eindhoven) header from the centre of the box is close, but misses to the left. Assisted by Phillipp Mwene.
Substitution, Rangers. Fashion Sakala replaces Antonio-Mirko Colak.
Attempt missed. Armando Obispo (PSV Eindhoven) left footed shot from the left side of the box is high and wide to the left. Assisted by Cody Gakpo.
Hand ball by John Lundstram (Rangers).
Foul by Ibrahim Sangaré (PSV Eindhoven).
Antonio-Mirko Colak (Rangers) wins a free kick on the right wing.
Marco van Ginkel (PSV Eindhoven) is shown the yellow card for a bad foul.
Foul by Marco van Ginkel (PSV Eindhoven).
James Sands (Rangers) wins a free kick in the defensive half.
Substitution, PSV Eindhoven. Marco van Ginkel replaces Philipp Max.
Armando Obispo (PSV Eindhoven) is shown the yellow card for a bad foul.
Foul by Armando Obispo (PSV Eindhoven).
Scott Wright (Rangers) wins a free kick on the right wing.
Attempt blocked. Carlos Vinícius (PSV Eindhoven) left footed shot from outside the box is blocked. Assisted by Cody Gakpo.
Foul by Carlos Vinícius (PSV Eindhoven).