Goal from Jon Daly, Fraser Aird and Bilel Mohsni proved sufficient for Ally McCoist's men to extend their lead at the summit of Scotland's third tier by 16 points over Dunfermline Athletic - who were held to a 1-1 draw with Forfar - and record their 15th straight league win in the process.
United, who have failed to secure victory at Rangers since 1959, were handed an uphill task in their bid to eradicate the status quo after just 12 minutes, as Irishman Daly rose highest to nod home Ian Black's free kick.
The Gers made further inroads toward achieving the 20-game winning streak 11 minutes later when Fraser Aird galloped towards goal before unleashing a fierce effort that sailed past goalkeeper David Hutton.
Mohsni wrapped up the points six minutes from time, smashing home from close range after the ball fell to his feet from Lee McCulloch's blocked effort.
The Glaswegians travel to Stenhousemuir in Scottish League One next week in a bid to extend their winning run to 21 matches.