Dado Prso gave Rangers an early lead, and two goals in five minutes from Fernando Ricksen and Nacho Novo midway through the second-half secured the points for the home side.
Rangers survived an early scare when Marvin Andrews' clearance fell to Burton O'Brien, but the midfielder's shot from 20 yards was just too high.
Livingston keeper Roddy McKenzie produced a brilliant finger-tip save to block Prso's header on the line from Thomas Buffel's cross, but the Croatian striker was not to be denied for much longer.
New signing Sotirios Kyrgiakos played through a superb 40-yard pass which beat the offside trap allowing Prso the time to collect and turn before steering his shot beyond McKenzie.
The Greek defender was using the ball intelligently from the back, and Novo nearly capitalised on one of his passes. The little striker did well to fend off Emmanuel Dorado's challenge before testing the visitors' keeper with a powerful shot.
Bojan Djordjic limped off with a groin strain on the half hour mark to be replaced by Hamed Namouchi. Mark Wilson was off-target with a rare effort for the visitors after appearing to foul Ricksen in the build-up.
Novo struck a powerful effort from 18 yards after Prso's clever lay-off, but McKenzie produced another excellent stop. From the resultant corner Krygiakos forced the Livingston keeper into a good block at his post before Buffel shot into the side netting when he should have done better.
McGregor had to look sharp to save bravely at the feet of Lilley after Andrews and Maurice Ross had made a mess of a clearance.
Namouchi wasted a fine chance before Prso sent Novo away with a clever chip which ended in the Spaniard being brought down by Dorado just outside the penalty box,resulting in a booking for the defender.
Ricksen made the punishment even more severe when he curled his free-kick high into the top corner from 20 yards.
Rangers made it three when Novo was on hand to turn home Buffel's wayward shot after good work by Prso on the flank.
Rangers could easily have added more with Alex Rae unlucky with a 35-yard effort which drifted narrowly wide after McKenzie had been caught out of position.
Livi manager Richard Gough was happy that Livi never got a tanking off Rangers today, he said -
"I have been here playing for Rangers and given some teams some real tankings," he said.
"It could have been worse as our goalkeeper made three or four magnificent saves in the first half.
"It is a bonus that the Dundee teams drew as that keeps them both down there at the bottom with us. Games against teams like that are more important."