Strikers Kris Boyd and Dado Prso each scored twice as the score flattered Rangers against brave Livingston.
Boyd celebrates his early goal at Ibrox
On eight minutes, Boyd rifled home from seven yards after a Peter Lovenkrands shot rebounded into the striker's path.
Wes Hoolahan and Paul Dalglish wasted chances for Livi before Gabor Vincze levelled with a fantastic strike.
But Boyd turned on a Thomas Buffel pass to stab Rangers back in front and Prso blasted in a free-kick before drilling another home an impressive late shot.
Rangers were the superior side and created more chances but Livingston were always in the game until Prso's late double.
The home side were guilty of slowing the game down after taking an early lead and only really woke up when the visitors equalised.
Lovenkrands tested Livingston goalkeeper Roddy McKenzie in the first few minutes and the Dane had a hand in the opening goal.
His shot cannoned off a defender and fell kindly to the feet of Boyd, who found the net with a quick reaction shot.
Lovenkrands then hooked wildly past the post, before Buffel was denied by a top-drawer save from McKenzie.
Early in the second-half, Lovenkrands sent a looping header just over the crossbar.
Hoolahan and Dalglish threatened the Rangers goal before the home fans were stunned by a great finish.
Vincze burst through the middle of a static defence and slotted past goalkeeper Ronald Waterreus after 52 minutes.
The Ibrox side's response was immediate and Lovenkrands unleashed a powerful, long-range drive which McKenzie just managed to touch away.
But Boyd settled the Rangers nerves when he picked up a reverse pass from Buffel before lashing the ball home.
A header from Vincze grazed the side-netting and Rangers were in need of another goal.
A delicate touch from substitute Prso sent Buffel into the penalty box but the Belgian international fired over.
It was left to Prso to hand his team-mates a lesson in finishing when he drilled home a free-kick from the edge of the area with a minute to go, before grabbing his second of the day with a low drive seconds later.
Rangers: Waterreus, Ricksen, Andrews, Kyrgiakos (Smith 45), Murray, Burke, Malcolm, Ferguson, Buffel, Kris Boyd (Novo 80), Lovenkrands (Prso 63). Subs Not Used: Klos, Hemdani, Hutton, Lowing.
Goals: Kris Boyd 8, 56, Prso 89, 90.
Livingston: McKenzie, Mackay, Tierney, Pinxten, Strong, McNamee (Walker 68), Brittain, Vincze, Hoolahan (Dair 86), Dalglish (Snodgrass 72), Hislop. Subs Not Used: Roy, Scott, Boyd, Dorrans.
Booked: McNamee, Vincze, Strong. Goal: Vincze 52.
Ref: E Smith