Paul Paton opened the scoring from close range on the stroke of half-time following a keenly contested first half.
United had breathing space in the 56th minute as Nadir Ciftci converted on the rebound when Mario Kello kept out Charlie Telfer's strike.
Telfer then completed the scoring with a cool finish on the end of Aidan Connolly's excellent pass 17 minutes from time.
Jackie McNamara's side are top at the expense of Hamilton Academical, who salvaged a thrilling 3-3 draw with Partick Thistle.
But Partick's fightback began in the 32nd minute as Jordan McMillan's effort found the net via a significant deflection off Grant Gillespie, and James Craigen hauled the visitors level with 22 minutes to play.
Christie Elliott struck left-footed and looked to have completed a remarkable comeback, but Hamilton's French midfielder Tony Andreu drove home his seventh goal of the season in the final minute.
A Gavin Stewart brace either side of David Clarkson's fifth goal in as many league outings proved decisive, with Alexei Eremenko on target for the hosts.
