Livingston put up a spirited display at Ibrox but fell to a wonderful late finish from Scott Arfield as Rangers maintained their four point lead at the top of the Scottish Premiership.
The Lions had frustrated their hosts for most of the game but Arfield popped up with the only goal of the game 15 minutes from time to crush his hometown team's hopes.
As expected, Rangers controlled much of the play and dominated possession but a gritty defensive display from David Martindale's men kept the champions at bay until Arfield expertly flicked a Borna Barisic pass over Max Stryjek and into the far corner.
Alex Lowry had the hosts' first chance but fired straight at Stryjek - who was later beaten by a fizzing Scott Wright strike only for Jack Fitzwater to hook the attempt off the line and keep the scores level.
The Lions had strong appeals for a penalty turned down when a Jack Fitzwater header was parried to Allan McGregor with referee Don Robertson ruling the ball must have hit the defender's chest and not his arm.
Genuine chances were at a premium for Rangers but Fashion Sakala went close as he got on the end of a James Tavernier delivery but Stryjek pulled off a smart save with his legs to deny the striker.
The Zambian ace showed neat footwork in the second half with a clever touch that took him away from a tackle before he charged at the Livi defence but couldn't keep his effort down as he blazed over the bar.
With the visitors continuing to frustrate the home side, substitute Arfield proved the late matchwinner. Sakala and Barisic exchanged passes down the left flank before the Croatian teed up the veteran midfielder who produced a clever flicked effort that looped over the defence and Stryjek.
The Lions passed up a late chance to equalise as Ayo Obileye couldn't connect and they had to return home empty-handed despite a fine showing in Glasgow.
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