A penalty from the captain was the difference at the break and was followed in the second-half by a superb free-kick before Kemar Roofe rounded off the scoring for the day with a close-range finish.
Manager Michael Beale named four changes to his side from last weekend’s Scottish Cup victory over Partick Thistle as Connor Goldson, Ryan Kent, Fashion Jr and Alfredo Morelos returned to the starting XI in place of James Sands, Ianis Hagi, Malik Tillman and Antonio Colak.
That meant Gers started at the Tony Macaroni Arena with Allan McGregor in goal and a back four of James Tavernier, Connor Goldson, Ben Davies and Borna Barisic.
Glen Kamara, Nicolas Raskin and Todd Cantwell were in midfield, with Ryan Kent, Fashion Jr and Alfredo Morelos up front.
Rangers looked to find the breakthrough with a series of corners inside the opening five minutes. The first was taken short, with Borna Barisic delivering into the back post in search of Connor Goldson but the ball was turned behind for another corner.
From the other side, James Tavernier whipped an inviting ball into the box but the danger was cleared by Livingston before space opened up for the Rangers captain to try a long-range effort but it dipped just over the crossbar.
Inside the opening 10 minutes, Rangers had the ball in the back of the net as Glen Kamara found the run of Alfredo Morelos on the left. The Colombian delivered the ball across goal with Fashion Jr turning it beyond Shamal George in the Livingston goal but the linesman raised his flag for offside.
Tavernier tried another strike from distance as Michael Beale’s side continued to search for the breakthrough in Livingston as he found the target but Shamal George saved the low effort.
With 23 minutes on the clock, Rangers were awarded a penalty following a VAR check. Referee David Dickson was called to review footage as James Penrice pulled the shirt of Alfredo Morelos as the striker rose to get a header away in the box.
After watching the footage, the referee pointed to the spot with James Tavernier stepping up and giving Rangers the advantage with a strong right-footed penalty - his 50th career goal from the spot.
At the other end, from a long throw-in from Livingston, the ball was directed across the face of goal with James Penrice unable to get a connection at the back post.
Fashion Jr was denied a goal early in the second-half as his powerful strike was blocked well by George before Livingston managed to clear the danger.
Stephen Kelly had a hit from distance as Livingston tried to find a route back into the game but it was held comfortably by Allan McGregor. Shortly after, Livingston captain Nicky Devlin delivered a ball into the box which Kelly hit on the volley but couldn’t keep his shot on target.
It was a lively couple of minutes as James Tavernier found the run of Ryan Kent to release the winger one-on-one with the goalkeeper but George was off his line quickly to deny.
Michael Beale made his first change of the afternoon as he came on to replace Fashion Jr. Roofe was involved instantly as he latched on the end of a ball from Todd Cantwell but it was just inches wide of the target.
Livingston were reduced to 10-men with just over 10 minutes of the game remaining as Stephane Omeonga was shown a second yellow card for a foul on the edge of the box on Kemar Roofe.
James Tavernier stood over the free-kick and set his eyes on the target as the captain struck the ball perfectly into the top corner for his second goal of the afternoon.
Rangers added a third in the final five minutes of the match as Kemar Roofe got on the scoresheet. Borna Barisic delivered a free-kick into the box which Roofe initially got a header on but it was blocked before Ben Davies also saw a strike blocked. With the ball still alive in the box, Roofe pounced on the rebound from Davies’ effort to finish beyond George.
With a few minutes of the game remaining Beale made a further three changes to his side, with 16-year-old Bailey Rice coming on to make his first-team debut in place of Nicolas Raskin. James Sands and Scott Wright were also introduced for Ryan Kent and Glen Kamara.
RANGERS: McGregor, Tavernier, Goldson, Davies, Barisic, Kamara (Sands,87), Raskin (Rice, 87), Cantwell, Kent (Wright, 78), Fashion Jr (Roofe, 67), Morelos (Colak, 78).
Subs not used: McLaughlin, King, Devine, Lovelace.
Livingston: George, Devlin, Fitzwater, Obileye, Penrice (Montano, 68), Sean Kelly (Shinnie, 54), Pittman , Omeonga, Bradley (Holt, 52), Stephen Kelly (Guthrie, 68), Nouble.
Subs not used: Hamilton, Longridge, Bahamboula, De Lucas, Guthrie, Boyes.