Rangers won comfortably enough in the end but this was a far from convincing performance by the Ibrox side.
Two late goals by Stephen Hughes and Shota Arveladze put the gloss on the scoreline to add to the first half goals from Prso and Hughes.
Livingston were far from dangerous opponents but for spells, especially in the second half, they controlled the midfield which must now be a worry for Alex McLeish. The manager however could point in mitigation to their stressful midweek game in Moscow on Champions League duty.
Rangers made the early breakthrough they so desperately wanted when Dado Prso netted from close range. After Nacho Novo had been fouled, Gregory Vignal's free kick found Arveladze at the near post but his header was cleared off the line by David McNamee. However Alex Rae returned the header from the edge of the box and found the striker who made no mistake.
The Rangers attack was combining well and from one Arveladze flick the ball bounced just beyond Novo and Roddy McKenzie in the Livingston goal was able to gather.
Novo's pace often embarrassed Scott McLaughlin on the Livingstone flank, but the winger's cross was just beyond Arveladze's reach, though Peter Lovenkrands following up should have been better than to blaze wildy over.
Stephen Hughes lined up a chance for Lovenkrands but his powerful shot was too close to the Livingston keeper.
The home side went two ahead with a marvellous goal after an outrageous flick by Arveladze. The Georgian's back-heel fooled three Livingston defenders and when Lovenkrands' first cross was returened to him by Prso, his second proved more productive as Hughes swept the ball home from six yards.
The home side were now in total control with Novo running the ball when he should have perhaps looked to pass the ball to Prso.
The start of the second half was very slack with Arveladze wasting good possession with a slack pass which failed to find Prso.
Rangers appeared content to sit on their lead and Livingston gradually started to threaten, especially when former Rangers player Steven Boyack advanced and challenged before unleashing a 20-yard-shot which scraped past Stefan Klos's post.
Rangers headed a third with their first indirect effort of the second half. From Arveladze's cut back substitute Steve Thompson mis-hit his shot completely but it fell kindly to Hughes who slid the ball home.
Arveladze finished off the scoring two minutes from time when he was on his own at the back post to prod home a Paolo Vanoli cross.
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