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Scott Arfield came off the bench to end Ross County's comeback bid as Rangers averted a second successive Scottish Premiership slip-up.
Jordan White's late penalty gave County hope before Arfield made sure of a deserved win for the champions.
Steven Gerrard's men, beaten by Dundee United in their previous league outing, had surged ahead with an exquisite Joe Aribo strike and Connor Goldson header.
Harry Clarke responded after Alfredo Morelos restored the two-goal margin.
Rangers move a point off the top and the performance will provide encouragement ahead of the second leg of their Europa League play-off against Alashkert.
Their next league assignment is the opening Old Firm derby of the season, while County remain winless after their opening three league games under new manager Malky Mackay.
County have never beaten Rangers and hadn't managed a goal in the previous six meetings - all defeats - but were aggrieved not to be given an early penalty when Alex Iacovitti's header hit Leon Balogun's arm.
Rangers made the most of the let-off with a rampant start and Aribo opened his scoring account for the season with a wonderful finish arced into the top corner.
Goldson's first goal since January soon followed, with the defender sending a downward header from a corner in off the post.
It looked a matter of how many Rangers would score and County were doing themselves no favours.
Goldson had another free header from a corner scrambled off the line and home goalkeeper Ross Laidlaw made amends for gifting possession to Steven Davis by shovelling an Ianis Hagi drive wide.
Mackay's men had been overrun, but hauled themselves level when Clarke, on loan from Arsenal, marked his first start by slamming home the rebound after Allan McGregor saved well from White.
It was scarcely deserved, but a self-inflicted blow after the restart gave County a mountain to climb again. Jordan Tillson's awful clearance from a Calvin Bassey cross went straight to Glen Kamara and the Finn fed shuttled the ball to Morelos for a scuffed finish into the far corner.
Again, though, the hosts back right back at Rangers. Allan McGregor kept out a stinging Blair Spittal effort, but Regan Charles-Cook's attempt on the rebound hit Calvin Bassey on the arm and White clinically converted from the spot.
Enter Arfield to calm Rangers nerves, following up after Laidlaw could only parry an angled drive from Morelos.
Arfield and Ryan Kent threatened a fifth as Rangers ended in the same dominant fashion they had started.
More to follow.
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Ross County
Squad number1Player nameLaidlaw
Squad number2Player nameRandall
Squad number20Player nameClarke
Squad number16Player nameIacovitti
Squad number24Player namePaton
Squad number4Player nameCancola
Squad number22Player nameTillson
Squad number8Player nameCallachan
Squad number17Player nameCharles-Cook
Squad number7Player nameSpittal
Squad number26Player nameWhite
Squad number10Player nameSamuel
Squad number23Player nameHungbo
Rangers
Squad number1Player nameMcGregor
Squad number2Player nameTavernier
Squad number6Player nameGoldson
Squad number26Player nameBalogun
Squad number3Player nameBassey
Squad number17Player nameAribo
Squad number10Player nameDavis
Squad number18Player nameKamara
Squad number7Player nameHagi
Squad number20Player nameMorelos
Squad number14Player nameKent
Squad number4Player nameLundstram
Squad number25Player nameRoofe
Squad number37Player nameArfield
Line-ups
Ross County
Formation 4-5-1
- 1Laidlaw
- 2RandallBooked at 50mins
- 20Clarke
- 16Iacovitti
- 24Paton
- 4CancolaSubstituted forHungboat 70'minutesBooked at 72mins
- 22Tillson
- 8Callachan
- 17Charles-CookSubstituted forSamuelat 90'minutes
- 7Spittal
- 26White
Substitutes
- 9Shaw
- 10Samuel
- 11Robertson
- 15Watson
- 23Hungbo
- 25Donaldson
- 31Maynard-Brewer
Rangers
Formation 4-3-3
- 1McGregor
- 2Tavernier
- 6Goldson
- 26Balogun
- 3BasseyBooked at 77mins
- 17AriboBooked at 37minsSubstituted forRoofeat 83'minutes
- 10Davis
- 18KamaraSubstituted forLundstramat 74'minutes
- 7HagiSubstituted forArfieldat 78'minutes
- 20Morelos
- 14Kent
Substitutes
- 4Lundstram
- 5Helander
- 11Itten
- 16Patterson
- 25Roofe
- 28McCrorie
- 37Arfield
Live Text
Match ends, Ross County 2, Rangers 4.
Second Half ends, Ross County 2, Rangers 4.
Corner, Rangers. Conceded by Ross Laidlaw.
Attempt saved. Ryan Kent (Rangers) left footed shot from the right side of the box is saved in the bottom left corner. Assisted by Scott Arfield.
Attempt saved. Leon Balogun (Rangers) header from the centre of the box is saved in the centre of the goal. Assisted by James Tavernier with a cross.
Corner, Rangers. Conceded by Ross Laidlaw.
Attempt saved. Scott Arfield (Rangers) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by Connor Goldson.
Substitution, Ross County. Dominic Samuel replaces Regan Charles-Cook.
Attempt saved. Leon Balogun (Rangers) header from the centre of the box is saved in the bottom left corner. Assisted by James Tavernier with a cross.
Corner, Rangers. Conceded by Ben Paton.
Ryan Kent (Rangers) wins a free kick in the attacking half.
Foul by Ross Callachan (Ross County).
Goal! Ross County 2, Rangers 4. Scott Arfield (Rangers) right footed shot from the centre of the box to the bottom left corner.
Substitution, Rangers. Kemar Roofe replaces Joe Aribo.
Attempt missed. Joseph Hungbo (Ross County) left footed shot from outside the box is high and wide to the left. Assisted by Blair Spittal.
Foul by John Lundstram (Rangers).
Blair Spittal (Ross County) wins a free kick in the defensive half.
Substitution, Rangers. Scott Arfield replaces Ianis Hagi.
Goal! Ross County 2, Rangers 3. Jordan White (Ross County) converts the penalty with a right footed shot to the bottom right corner.
Calvin Bassey (Rangers) is shown the yellow card for hand ball.