Goals from Gary-Mackay Steven, Stuart Armstrong, Ryan Gauld and Nadir Ciftci capped an excellent display from United with Ivan Sproule and Rocco Quinn netting for the home side.
United created the game's first clear-cut opportunity when County goalkeeper Mark Brown was forced to tip Ciftci's 30-yard free kick over the bar.
County hit back with a shot from Rocco Quinn which was gathered easily by Radoslaw Cierzniak, but it was the visitors though who broke the deadlock in the 18th minute.
Ross County old-boy Mackay-Steven raced onto Paul Paton's searching ball and was brought down by a clumsy challenge in the penalty area from Brown.
Mackay-Steven made no mistake from his spot-kick as he stepped up to calmly send Brown the wrong way slotting the ball into the bottom left-hand corner of the net.
The visitors extended their lead a minute later when Gauld and Ciftci linked up well on the right to cross for Armstrong to loop his header over the stranded Brown.
County almost pulled one back when Richard Brittain's deflected free kick was palmed onto the post by Cierzniak, but United raced into a 3-0 lead in the 40th minute.
Armstrong delicately passed to Gauld who beat the offside trap before showing great composure to sweep home past the on-rushing Brown.
County tried to force their way back into the contest and Graham Carey's measured cross was met by Stuart Kettlewell whose header came back off the post just before half-time.
United came out strong after the break and in the 48th minute Brown spilled Ciftci's shot but Gauld was unable to latch onto the rebound.
Ciftci should have made it four after being played in by Mackay-Steven, but the County goalkeeper palmed his shot away for a corner.
Ciftci was not to be denied however, and he claimed a fourth for the away side in the 65th minute when he rounded Brown slotting home after latching on to a Gauld through ball.
The home side managed to pull one back after 71 minutes when Sproule's cross took a wicked deflection leaving Cierzniak no chance as the ball sailed over his head.
Minutes later, another dangerous cross from Carey allowed Rocco Quinn to head home setting up an exciting final fifteen minutes.
With County growing in confidence, Quinn had a shot saved by Cierzniak before Brittain had an effort deflected for a corner with the United keeper beaten.
County created one more chance through Melvin De Leeuw, but it was the visitors who claimed three points sealing their second of the season and elevating them to fifth place in the Scottish Premiership.