That Rangers won by only three goals was testament to Livingston's fighting spirit, though Richard Brittain took that rather too literally when he was red-carded in the 75th minute for a wild retaliatory tackle on Ian Murray.
Goals by Dado Prso, Jose Pierre-Fanfan and a late effort by Peter Lovenkrands were enough to send the home fans away satisfied.
Rangers were slow to warm up but in the 12th minute a good turn and run by Prso set up Barry Ferguson, who pulled his shot wide.
Dubravko Tesevic and Allan Walker shot wide from long range before Nacho Novo's cross was desperately hacked clear at the expense of a corner by Manu Dorado.
Rangers made the breakthrough midway through the first half. Lovenkrands' cross was cleared to Alex Rae, whose powerful shot from outside the box was parried by Roddy McKenzie before Prso lashed the rebound high into the net.
Rangers made the game safe early in the second half when Prso at the near post glanced a Lovenkrands cross to the back post and though the ball appeared to be spinning in, Fanfan made sure.
After Brittain's dismissal there was no way back for Livingston but it took until the last minute for Rangers to score the third goal which put them top of the table.
Lovenkrands cut inside past three defenders before shooting low past the keeper.