An utterly dominant display from Mark Warburton’s men saw them stretch their lead at the Championship summit to six points.
Despite the wintry conditions, the hosts bossed the game from the off and opened the scoring after eight minutes through the unlikely figure of Danny Wilson.
The defender nodded into an empty net after debutant goalkeeper Mar McCallum had initially saved a Martyn Waghorn effort.
Waghorn doubled their advantage on 21 minutes when he converted from the penalty spot after Kenny Miller was brought down in the box.
It was Miller who netted Rangers third and his 11th of the season ten minutes before the break when he curled a shot into the corner after neat play from Lee Wallace.
And Wallace was provider for Rangers fourth when his shot was deflected into the path of Waghorn who subsequently lofted the ball over McCallum to score his 27th goal of the campaign.
The second-half was over as a contest although Livingston put on a better showing and scored a consolation courtesy of an angled strike from substitute Liam Buchanan.
Andy Halliday missed a late penalty for the Light Blues but altogether it was a good afternoon’s work for the Championship leaders.
A delighted Mark Warburton said afterwards
“It was difficult weather conditions for both teams but I thought we played excellent in the first half we created chance after chance, we dominated the football and could’ve scored more.
“We were a bit lacklustre and a bit flat (in the second half) but the job was done by half-time.”
Meanwhile Livi manager David Hopkin was also pleased with his side’s response in the second period.
“I thought the first half we were overwhelmed, Rangers started at a great tempo and we struggled to cope.
“But I’m taking the positives, we won the second half 1-0 and that’s all I’m looking for.”