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Rangers held off Livingston's fightback to maintain their Scottish Premiership lead on Giovanni van Bronckhorst's first league match in charge.
Scott Arfield and Joe Aribo scored fine goals in the first 16 minutes to put the visitors firmly in command.
Bruce Anderson responded for Livingston before the break but Fashion Sakala killed off their challenge.
Victory moves Rangers six points clear of Hearts in second place and seven ahead of Celtic.
However, Ange Postecoglou's side have the chance to get back to four points behind when they face Aberdeen at 15:00 GMT on Sunday.
Van Bronckhorst got his first win with his first match in charge on Thursday night against Sparta Prague and made just one change as Arfield replaced Steven Davis in midfield.
The Canada international's familiar trait of running in behind from deep opened up the chance for the first goal as he ghosted in between two of Livingston's three centre-backs to collect James Tavernier's clever pass and scoop the ball over Max Stryjek into the net.
Livingston were opened up again soon after as Ryan Kent kept his width on the left flank as the ball went to the right-hand side, and he was able to receive a diagonal switch before feeding Morelos, who teed up Aribo to sweep a brilliant finish off the under side of the bar and in.
Livingston looked rattled but were able to take advantage of Rangers' ongoing slackness at the back this term. Jack Fitzwater arrowed a long ball in behind Connor Goldson for Alan Forrest, and Anderson pounced to head home when his team-mate's shot was saved.
The response drained the tempo from Rangers' game and goalkeeper Allan McGregor had to stretch to push Forrest's back-post shot over the bar before the break as Borna Barisic stood off and allowed Bailey's cross to arrive.
Despite a near 10-minute delay to the second half after Rangers fans threw snowballs on to the pitch, both teams initially upped the pace after the break and Stryjek had to deny Hagi, Kent, and Aribo.
However, Livingston managed to stay in the fight, up until the final 12 minutes when substitute Sakala capitalised to head in Rangers' third after Stryjek misjudged Tavernier's corner.
Man of the match - Ryan Kent
What did we learn?
Van Bronckhorst has picked up from Steven Gerrard without a hitch so far, but there were a few of the same hints of change from Thursday. The use of Kent and Hagi as more traditional wingers rather than the usual number 10s was evident again in the first period, and the former's width was crucial to the second goal as switches of play proved effective.
Hagi picked up clever positions between Livingston's centre-backs and left-wing back and looks like he will get plenty of time to build consistent form under the new manager. Bringing Nathan Patterson on to replace him again suggests the Scotland full-back may be in for more game time too.
Defence is still an issue for Rangers, though, and they have now conceded more goals in their first 14 league games than they did in the whole of last season. Even if last term was a freakish effort, solidity remains a problem.
Livingston's goal came from a diagonal ball into the space between Goldson and the advanced Tavernier, and the former was erratic in possession on a few occasions in the first half. Barisic seems to stay back more often to help, though the Croatian was more influential in attack after the break.
As for Livingston, David Martindale was marking a year in charge and he can be relatively pleased with his side's efforts, bar a disjointed first 20 minutes when they were erratic and fell two goals behind.
Stephane Omeonga battled well in midfield, Anderson put in a great shift up front and they hung in there for long spells. However, the manager would have wanted to see more from his team in attack as they faded after a fast start to the second half.
What's next?
Both sides begin a busy December fixture schedule with away trips in the Premiership. Rangers face their League Cup conquerors Hibernian on Wednesday (19:45 GMT), while Livingston play Aberdeen at the same time.
How to play
Rate players out of 10 throughout or after the game. The rater will close 30 minutes after the final whistle.
Rating range key1 = Give it up10 = Pure perfection
Livingston
Squad number32Player nameStryjek
Squad number2Player nameDevlin
Squad number5Player nameFitzwater
Squad number4Player nameParkes
Squad number21Player nameMcMillan
Squad number18Player nameHolt
Squad number33Player nameOmeonga
Squad number17Player nameForrest
Squad number14Player nameBailey
Squad number11Player nameCristian Montaño
Squad number9Player nameAnderson
Squad number22Player nameShinnie
Squad number29Player namePenrice
Squad number37Player nameKabia
Rangers
Squad number1Player nameMcGregor
Squad number2Player nameTavernier
Squad number6Player nameGoldson
Squad number3Player nameBassey
Squad number31Player nameBarisic
Squad number18Player nameKamara
Squad number17Player nameAribo
Squad number7Player nameHagi
Squad number37Player nameArfield
Squad number14Player nameKent
Squad number20Player nameMorelos
Squad number9Player nameDefoe
Squad number16Player namePatterson
Squad number30Player nameSakala
Line-ups
Livingston
Formation 3-4-2-1
- 32Stryjek
- 2DevlinBooked at 45mins
- 5Fitzwater
- 4Parkes
- 21McMillanSubstituted forPenriceat 59'minutes
- 18Holt
- 33OmeongaBooked at 69mins
- 17ForrestBooked at 31mins
- 14BaileySubstituted forKabiaat 80'minutes
- 11Montaño
- 9AndersonSubstituted forShinnieat 59'minutes
Substitutes
- 3Longridge
- 10Sibbald
- 15Panayiotou
- 22Shinnie
- 29Penrice
- 36Maley
- 37Kabia
Rangers
Formation 4-2-3-1
- 1McGregor
- 2Tavernier
- 6Goldson
- 3Bassey
- 31Barisic
- 18Kamara
- 17Aribo
- 7HagiSubstituted forPattersonat 73'minutes
- 37ArfieldBooked at 9mins
- 14KentSubstituted forSakalaat 73'minutes
- 20MorelosSubstituted forDefoeat 90+2'minutes
Substitutes
- 4Lundstram
- 9Defoe
- 10Davis
- 16Patterson
- 23Wright
- 30Sakala
- 33McLaughlin
Live Text
Match ends, Livingston 1, Rangers 3.
Second Half ends, Livingston 1, Rangers 3.
Foul by Glen Kamara (Rangers).
Jason Holt (Livingston) wins a free kick in the defensive half.
Attempt saved. Jermain Defoe (Rangers) right footed shot from outside the box is saved in the bottom left corner. Assisted by Scott Arfield.
Foul by Nathan Patterson (Rangers).
Andrew Shinnie (Livingston) wins a free kick in the defensive half.
Substitution, Rangers. Jermain Defoe replaces Alfredo Morelos.
Attempt saved. Scott Arfield (Rangers) right footed shot from outside the box is saved in the bottom left corner. Assisted by Alfredo Morelos.
Attempt blocked. Jason Holt (Livingston) right footed shot from outside the box is blocked.
Foul by James Tavernier (Rangers).
Cristian Montaño (Livingston) wins a free kick on the left wing.
Joe Aribo (Rangers) wins a free kick in the attacking half.
Foul by Stephane Omeonga (Livingston).
Offside, Livingston. Jack Fitzwater tries a through ball, but Jaze Kabia is caught offside.
Attempt saved. Alfredo Morelos (Rangers) left footed shot from outside the box is saved in the bottom right corner. Assisted by Glen Kamara.
Substitution, Livingston. Jaze Kabia replaces Odin Bailey.
Goal! Livingston 1, Rangers 3. Fashion Sakala (Rangers) header from very close range to the high centre of the goal. Assisted by James Tavernier with a cross following a corner.
Corner, Rangers. Conceded by Tom Parkes.
Attempt blocked. Fashion Sakala (Rangers) left footed shot from very close range is blocked. Assisted by Alfredo Morelos.