Substitute Max Aarons latched onto a loose ball and lashed it past Jerome Prior deep into injury time to earn Rangers their first win of the season in the Scottish Premiership at their sixth attempt.
The goal, following a corner on the right, sparked celebrations on the terraces around three of the four sides in the ground. Livingston fans felt deflated after a strong performance.
The home side went behind after 23 minutes when James Tavernier volleyed home from close after an Oliver Antman cross to break the deadlock in an entertaining tussle in beautiful Autumnal conditions at the Home of the Set Fare arena.
Minutes later, the struggling Ibrox men could have doubled their lead but razor-sharp Prior saved a penalty kick from Tavernier after industrious Nicolas Raskin had his shirt tugg