James Tavernier gave Russell Martin’s side the lead in the first-half, before Mo Sylla equalised for the hosts with 20 minutes remaining.
However, Rangers battled for the victory with a huge first goal for Aarons securing the three points.
There were three changes from midweek as Connor Barron, Oliver Antman and Bojan Miovski came into the starting line-up in place of Mohamed Diomande, Mikey Moore and Youssef Chermiti who were on the bench.
Rangers started with Jack Butland in goal behind a back four of James Tavernier, John Souttar, Derek Cornelius and Jayden Meghoma.
Barron joined Nico Raskin and Thelo Aasgaard in midfield, while Djeidi Gassama, Oliver Antman and Bojan Miovski completed the eleven.
Rangers supporters occupied three of the four stands at the Set Fare Arena as Nico Raskin got the action underway in West Lothian.
Jack Butland was called into action early as the home side looked to take advantage in this match. Stevie May raced down the right and sent a low shot towards goal which the Rangers number one was able to block.
May was involved again shortly after, as he laid the ball off to Lewis Smith on the edge of the area. He took a touch onto his left foot and curled a shot just wide of the target.
There was a big chance for Rangers with 13 minutes on the clock, as John Souttar sent a ball forward which Nico Raskin flicked into the path of Bojan Miovski. The striker had made a good run into the box and looked to lift a left-footed effort over the keeper but it was just high of the target.
It was Rangers who took the lead and captain James Tavernier who came up with the crucial breakthrough in Livingston with just over 20 minutes played. Nico Raskin sent the ball out wide to Djeidi Gassama who delivered a ball deep into the box. Oliver Antman was on hand to send it back across goal and Tavernier found a finish in style with a volley to beat Jerome Prior.
Shortly after, Rangers were awarded a penalty as Nico Raskin was brought down in the box by Stevie May as he attacked a Tavernier corner. After a VAR check, John Beaton pointed to the spot and the captain stepped up.
However, this time Jerome Prior denied Tavernier as he managed to get his feet to the penalty.
Rangers appeared to gain confidence from their lead, and Connor Barron was almost able to round off a lovely bit of play with a low drilled finish from just inside the box, but the Livingston goalkeeper did just enough to get a hand on it.
Prior had come up with some big moments in this first-half, and pulled off another good save as John Souttar struck towards goal from a James Tavernier corner but the keeper reacted to push away the goalbound effort.
Derek Cornelius thought he had found his first Rangers goal in the final minutes of the first-half as sent the ball into the back of the net from a James Tavernier free-kick, but it was disallowed after a VAR check for a handball in the build-up.
Into the second-half, Rangers were struggling to threaten Livingston in the same way as they were before the break, with the hosts growing into the game.
Stevie May threatened again with a right-footed strike just after the hour mark but it was turned behind by a crucial save from Jack Butland.
The equaliser Livingston had been threatening did come with 68 minutes played as the ball was whipped into the box by Adam Montomery and Mo Sylla managed to get a strong header to send it beyond Butland.
Martin turned to his bench as he looked to inject some freshness into his team, with Youssef Chermiti, Joe Rothwell and Max Aarons introduced for Oliver Antman, Thelo Aasgaard and Derek Cornelius, who appeared to have taken a knock.
Further changes followed with Nedim Bajrami and Mikey Moore introduced for the final 10 minutes, with the latter testing Prior with a curling effort but the goalkeeper managed to gather.
With eight minutes added on in injury time, there was still time for a winner in West Lothian.
A series of corners saw Rangers keep pushing for that crucial goal, with Prior producing another good save to tip over a Miovski header.
And with four minutes of injury time played Rangers got the goal they needed. The corner was swung into the box by James Tavernier and flicked down by Nico Raskin and it was a lovely finish from substitute Max Aarons with his first Rangers goal to secure the three points.
RANGERS: Butland, Tavernier, Souttar, Cornelius (Aarons, 72), Meghoma (Moore, 82), Raskin, Barron (Bajrami, 82), Aasgaard (Rothwell, 72), Gassama, Antman (Chermiti, 72), Miovski.
Subs: Kelly, Diomande, Djiga, Curtis.
Livingston: Prior, Montgomery, Susoho (Yengi, 89), Pittman, Smith (Carey, 89), Winter (McLennan, 65), May (Bokila, 75), Finlayson (Blaney, 65), Sylla, Tait, Wilson.
Subs: Hamilton, Muirhead, Robinson, Shinnie.