Victory took the Glasgow giants level on points with Hearts but ahead on goal difference.
The Edinburgh club, however, can regain top spot away to bottom-of-the-table Livingston on Sunday when third-placed Celtic - five points behind arch-rivals Rangers - face Dundee.
Rangers Striker Ryan Naderi opened the scoring on the half-hour mark with a close-range finish before defender Dujon Sterling doubled the lead four minutes before the break with his first league goal for the Gers.
United forward Amar Fatah pulled a goal back with a strike just before half-time, but Thelo Aasgaard restored the Light Blues' two-goal lead in the 52nd minute.
And substitute Zach Sapsford sparked fresh worry at Ibrox with a 72nd minute only for Bojan Miovski to come off the bench and put the result beyond courtesy of a deflected shot with five minutes of normal time remaining.
In other matches, fifth-placed Hibernian overwhelmed relegation-threatened Kilmarnock 3-0, mid-table Falkirk edged Motherwell 3-2 and St Mirren defeated fellow strugglers Aberdeen 2-0.