Jackie McNamara's side, who finished sixth last season, have not had the best start to the new campaign, losing twice including a 1-0 defeat against Celtic in their last league fixture.
Yet there was no way they were going to suffer the same fate at the hands of Ross as they moved 3-0 up before half-time with goals from Gary Mackay-Steven, Stuart Armstrong and Ryan Gauld.
Though the second half began in the same vein with Nadir Ciftci finding the back of the net, there was a late fightback from the hosts who saw Ivan Sproule and Rocco Quinn both score in the space of five minutes.
Both managers opted to field strong sides at Victoria Park after mixed starts to the new campaign and the class of United quickly shone through.
Mackay-Steven blasted home a penalty in the 18th minute after being brought down by County goalkeeper Mark Brown.
Armstrong was quick to build on the opener, heading past a bewildered Brown to leave Ross 2-0 down after just 20 minutes.
The hosts tried to respond, hitting the woodwork on two occasions, but were punished again for their defensive failings as Armstrong set up teenager Gauld to earn a three-goal advantage going into the break.
It did not initially look like a spell in the dressing room had done the home side any favours as Ciftci picked up his first goal of the new campaign in the 65th minute.
Derek Adams' side eventually managed to come back into the contest as the clock ran down but goals from Sproule, who was on target with a deflected cross, and Quinn proved too little, too late.
County now sit ninth and will hope to turn their fortunes around when they face Hearts at home next Saturday.
