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.
It looked like being plain sailing for the hosts as two goals in as many minutes from Darian MacKinnon and Danny Redmond gave them a 2-0 lead midway through the opening period.
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.
Champions Celtic replaced Inverness Caledonian Thistle in third as John Guidetti continued his hot streak in front of goal to seal a 1-0 win
The on-loan Manchester City striker took his tally to nine goals in his past seven appearances following a midweek hat-trick against Partick in the League Cup.
Inverness felt Ross Draper was fouled but Anthony Stokes broke forward in the 49th minute, setting up Guidetti to finish with aplomb.
Dundee climbed to sixth and to within one point of Kilmarnock, who they beat 3-1 to claim a third consecutive win.
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.
