A strike from Cyriel Dessers on 22 minutes gave the Light Blues - who also had two goals disallowed in the opening forty-five and missed a penalty – a slender advantage at the half-time interval.
James Tavernier, however, did make amends from the spot in the second half when his side were awarded their second penalty of the afternoon on 75 minutes, the skipper firing home with aplomb from 12 yards to complete the scoring in West Lothian.
The match started after a perfectly observed minute of silence, which included a stunning poppy display from the visiting Rangers fans behind Jack Butland’s goal.
And it was the Light Blues that immediately pushed forward with intent on Almondvale’s artificial pitch, with 20-year-old Ross McCausland – who impressed on his first senior start – getting a few important early touches and immediately asking questions of Livingston left-back James Penrice.
The first goal-scoring chance arrived on 12 minutes, with a moment of hesitancy from a Livi throw-in in front of the Gers dugout allowing Dessers to nip in and enter the 18-yard box. With his left foot and from a tight angle, the striker’s low effort was well blocked by the home side’s goalkeeper Shamal George.
Rangers did have the ball in the net four minutes later with Connor Goldson firing in from close range, but VAR ruled that Dessers was in an offside position when James Tavernier’s whipped free-kick was delivered into the danger area.
The pressure was relentless though, and on 23 minutes a jinking run from McCausland led to the youngster being brought down by George, who had sprinted off his goal-line and dived at his feet. Referee Steven McLean pointed to the spot but Tavernier uncharacteristically sent his penalty wide of target, to the relief of the home fans.
You felt it was only a matter of time before Rangers would take the lead, and they did just that with 26 minutes on the clock.
Tom Lawrence, from inside his own half, fed a brilliant pass to Dessers who sprinted clear of his marker to get a left-foot shot away. The ball took a deflection off a stretching Livi defender and spun over George before rolling into the net.
Livingston tried to battle back into the game but the Gers defence remained watertight, with a curling shot from Cristiano Montano, which was straight at Butland, their only real moment of note in a first half Rangers dominated.
On 43 minutes the ball was in the net again with McCausland producing a wonderfully-placed finish high beyond George, but the referee sadly halted his celebrations due to a foul in the box by Sima in the build-up.
Before the half-time whistle one more chance was created, with Dessers again finding space but George again denied the former Cremonese forward with another good save.
David Martindale decided to introduce former Rangers midfielder Jason Holt to his side for the restart, with Mo Sangare the player replaced.
Clement waited until the 58th minute to make his first change, with Danilo going on for Dessers during a break in play while Goldson and Montano received treatment following a clash of heads.
With the Rangers supporters giving the players on the pitch their full backing, the visitors had to be patient in possession as Livingston sat deep and tried to frustrate.
The second goal finally came on 75 minutes and this time Tavernier made no mistake from the penalty spot.
It was Livi captain Michael Devlin who was guilty of raising his arm in the box and connecting with the ball, and after the official had made the correct call Rangers’ captain was ice cool as he sent the George the wrong way to secure all three valuable points for his in-form side.
RANGERS: Butland, Tavernier, Goldson, Balogun, Barisic, Jack (Cifuentes 88), Lundstram, McCausland (Lammers 77), Lawrence (Cantwell 77), Sima (Ridvan 88), Dessers (Danilo 58)
SUBS NOT USED: McCrorie, Sterling, Roofe, Davies
GOALS: Dessers 26, Tavernier 77pen
BOOKINGS: Cantwell
LIVINGSTON: George, Montano (Brandon 88), Devlin, Pittman, Anderson, Nouble (Guthrie 78), Sangare (Holt 45), Shinnie, de Lucas (Parkes 69), Kelly, Penrice
SUBS NOT USED: Hamilton, Kelly, Welch-Hayes, Bradley, Lloyd
BOOKINGS: Montano
REF: Steven McLean