Thomas Buffel made the intial breakthrough and substitute Steven Thompson grabbed a second before Peter Lovenkrands made it nine goals in his last six games to end the scoring.
Rangers nearly conceded early when Collin Samuel's cross spun off Ian Murray on to the roof of the net. Marvin Andrews then headed the ball out only as far as Samuel as the Rangers defence looked nervous, but the United striker couldn't take advantage.
Alan Archibald then hit a 14-yard free-kick over the bar as United dominated the early exchanges. Rangers' first threat came when Nacho Novo found Barry Ferguson in the box, but his shot was deflected for a corner.
Rangers' keeper Ronald Waterreus could only parry a powerful Mark Wilson shot, but was grateful that Samuel was ruled offside as the striker latched on to a loose ball.
Rangers came more into the match towards the break. Buffel laid a superb pass to Ferguson but Derek Stillie did well to block his strike before Chris Burke's follow up was cleared.
There was a touch of luck about the opening goal when, from Alan Lowing's cross, Thompson headed down to Lovenkrands, who miscued his kick. However, the ball fell for Buffel to lash a left-foot shot high into the net.
It was a cruel break for United as Burke began to torment the visitors down the left. Good play by the winger ended with Buffel crossing for Thompson to nod home a simple header.
Thompson laid the ball off to Burke, whose cross was glanced home by Lovenkrands to continue his recent run of sparkling form.