Joe Aribo swept in Rangers' second goal after just 16 minutes
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.
- Reaction & as it happened
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 KentKent was influential as he stayed wide, and looks sharp after his return from injury. Tavernier grabbed another two assists to underline his consistencyWhat 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 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.
Kent and Hagi's heat map against Ross County (left) in Steven Gerrard's last game and Livingston (right) show the difference in widthWhat they said
Livingston manager David Martindale: "It is fair to say that Rangers deserved the three points. But we feel we could have taken something from the game because of the first 60-70 minutes.
"We probably created the better chances on the break, whereas Rangers kept the better of the possession. It's frustrating to concede from the set-piece."
Rangers manager Giovanni van Bronckhorst on Sky Sports: "We controlled the game and had a great start. We knew the chances would come if we ran into the spaces. It was a professional game from our point of view.
"We were a but sloppy at times and a bit slow. You have to make sure you have to finish the game. The header from Sakala was relief when it came at the time that it did."
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.
Player of the match
McGregorAllan McGregor
with an average of 8.79
- LivingstonLivingstonLivingstonRangersRangersRangers
LivingstonAvgSquad number32Player nameStryjekAverage rating
5.00
Squad number18Player nameHoltAverage rating
4.77
Squad number11Player nameCristian MontañoAverage rating
4.32
Squad number33Player nameOmeongaAverage rating
4.26
Squad number14Player nameBaileyAverage rating
4.17
Squad number22Player nameShinnieAverage rating
3.83
Squad number2Player nameDevlinAverage rating
3.79
Squad number9Player nameAndersonAverage rating
3.71
Squad number37Player nameKabiaAverage rating
3.47
Squad number21Player nameMcMillanAverage rating
3.47
Squad number4Player nameParkesAverage rating
3.47
Squad number5Player nameFitzwaterAverage rating
3.41
Squad number29Player namePenriceAverage rating
3.31
Squad number17Player nameForrestAverage rating
3.12
RangersAvgSquad number1Player nameMcGregorAverage rating
8.79
Squad number37Player nameArfieldAverage rating
8.26
Squad number17Player nameAriboAverage rating
8.21
Squad number30Player nameSakalaAverage rating
8.12
Squad number7Player nameHagiAverage rating
7.91
Squad number14Player nameKentAverage rating
7.82
Squad number16Player namePattersonAverage rating
7.48
Squad number18Player nameKamaraAverage rating
7.43
Squad number3Player nameBasseyAverage rating
7.40
Squad number2Player nameTavernierAverage rating
7.37
Squad number31Player nameBarisicAverage rating
7.30
Squad number20Player nameMorelosAverage rating
7.11
Squad number9Player nameDefoeAverage rating
6.69
Squad number6Player nameGoldsonAverage rating
6.28
- Line-upsMatch StatsLive Text
Line-upsLivingston
Formation 3-4-2-1
32Stryjek2Devlin5Fitzwater4Parkes21McMillan18Holt33Omeonga17Forrest14Bailey11Montaño9Anderson
- 32Stryjek2DevlinBooked at 45mins5Fitzwater4Parkes21McMillanSubstituted forPenriceat 59'minutes18Holt33OmeongaBooked at 69mins17ForrestBooked at 31mins14BaileySubstituted forKabiaat 80'minutes11Montaño9AndersonSubstituted forShinnieat 59'minutes
Substitutes
- 3Longridge10Sibbald15Panayiotou22Shinnie29Penrice36Maley37Kabia
Rangers
Formation 4-2-3-1
1McGregor2Tavernier6Goldson3Bassey31Barisic18Kamara17Aribo7Hagi37Arfield14Kent20Morelos
- 1McGregor2Tavernier6Goldson3Bassey31Barisic18Kamara17Aribo7HagiSubstituted forPattersonat 73'minutes37ArfieldBooked at 9mins14KentSubstituted forSakalaat 73'minutes20MorelosSubstituted forDefoeat 90+2'minutes
Substitutes
- 4Lundstram9Defoe10Davis16Patterson23Wright30Sakala33McLaughlin
Referee:David MunroAttendance:8,825Match StatsHome TeamLivingstonAway TeamRangersPossessionHome28%Away72%ShotsHome7Away20Shots on TargetHome4Away8CornersHome3Away7FoulsHome14Away12Live TextPost update
Match ends, Livingston 1, Rangers 3.
90'+4'Full Time
Second Half ends, Livingston 1, Rangers 3.
90'+4'Post update
Foul by Glen Kamara (Rangers).
90'+4'Post update
Jason Holt (Livingston) wins a free kick in the defensive half.
90'+3'Post update
Attempt saved. Jermain Defoe (Rangers) right footed shot from outside the box is saved in the bottom left corner. Assisted by Scott Arfield.
90'+2'Post update
Foul by Nathan Patterson (Rangers).
90'+2'Post update
Andrew Shinnie (Livingston) wins a free kick in the defensive half.
90'+2'Substitution
Substitution, Rangers. Jermain Defoe replaces Alfredo Morelos.
90'+1'Post update
Attempt saved. Scott Arfield (Rangers) right footed shot from outside the box is saved in the bottom left corner. Assisted by Alfredo Morelos.
87'Post update
Attempt blocked. Jason Holt (Livingston) right footed shot from outside the box is blocked.
87'Post update
Foul by James Tavernier (Rangers).
87'Post update
Cristian Montaño (Livingston) wins a free kick on the left wing.
85'Post update
Joe Aribo (Rangers) wins a free kick in the attacking half.
85'Post update
Foul by Stephane Omeonga (Livingston).
85'Post update
Offside, Livingston. Jack Fitzwater tries a through ball, but Jaze Kabia is caught offside.
83'Post update
Attempt saved. Alfredo Morelos (Rangers) left footed shot from outside the box is saved in the bottom right corner. Assisted by Glen Kamara.
80'Substitution
Substitution, Livingston. Jaze Kabia replaces Odin Bailey.
78'goalGoal!
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.
78'Post update
Corner, Rangers. Conceded by Tom Parkes.
76'Post update
Attempt blocked. Fashion Sakala (Rangers) left footed shot from very close range is blocked. Assisted by Alfredo Morelos.
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Source: bbc.com