Chris Sutton's early second half goal and Alan Thompson's superb late volley were enough to give The Bhoys all the points against a plucky Livingston.
The match started brightly with Jackie McNamara testing Roddy McKenzie, while at the other end Francisco Quino fired just over from outside the box.
Martin O'Neill's half-time team-talk had the desired effect and Sutton's exquisite touch and shot inside the penalty area after 48 minutes put the visitors ahead.
It was almost tow shortly after, but Henrik Larsson's goal-bound effort was escorted away from danger by Oscar Rubio from close-range.
Alan Thompson ensured the league leaders would not suffer a nervy ending after his clinical left-footed volley clinched a deserved win with five minutes remaining.
Rangers kept pace with leaders Celtic, but only after a close 2-1 victory over Dundee United at Ibrox.
Two goals in the space of three first half minutes from Nuno Capucho and Peter Lovenkrands put the home side in control.
Rangers failed to add to their advantage and they were given a scare shortly after the break when former Gers striker Billy Dodds pulled one back, but it proved no more than a consolation.
Dunfermline continued their impressive form following a 2-1 win over Hearts.
Derek Young put the home side ahead after 21 minutes, however former Leeds man Alan Maybury levelled matters before the break.
Scott Wilson netted what proved to be the winner shortly after the hour mark to clinch their sixth league win of the season.
Kilmarnock bagged all three points from their trip to Dundee thanks to Kris Boyd's goal in a 2-1 win.
Colin Nish fired the visitors ahead early on, only for Nacho Novo to level matters from the penalty spot.
The home side were not level for long with Boyd scoring what proved to be the winner just five minutes later.
SPL:
Dundee 1-2 Kilmarnock
Dunfermline 2-1 Hearts
Livingston 0-2 Celtic
Rangers 2-1 Dundee Utd
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