Victory for either side at Tannadice would have seen them climb to the top of the table and United appeared the most likely to succeed only to come up against a stubborn County defence.
County survived a muted penalty appeal after 56 minutes when Ross Tokely challenged Ryan Dow, who later chipped an effort on to the top of the bar, to keep a fifth clean sheet in six matches since being promoted to the top tier. It is now 13 months since County's last league defeat, the 5-1 loss at Hamilton on August 13, 2011.
The Irn-Bru First Division champions had made an impressive start to life in the top flight, conceding just once in their opening five matches, and that was during a 1-1 draw with SPL champions Celtic.
Colin McMenamin headed over following an early corner for County before the visitors were almost gifted an opener when a Keith Watson back-pass had Radoslaw Cierzniak toiling. The United goalkeeper mis-controlled the ball and it ricocheted off McMenamin and wide when it could have so easily gone in.
United striker Johnny Russell created an opportunity for himself out of nothing, wriggling his way through on the left side of the area to make space for a shot which Michael Fraser saved with his feet. Russell was quickest to the rebound but could only sweep the ball into the side-netting.
United began to take control of possession, but there were few chances until Michael Gardyne turned and found space on the edge of the area to curl a shot towards the far corner which Fraser, at full stretch, turned away.
In the second half, a long-range John Rankin effort went straight at Fraser before Tokely challenged Dow on the left side of the area and referee Willie Collum waved away penalty appeals, pointing instead for a goal kick as County withstood further pressure.
Fraser beat Rankin to a long ball forward as United again tried to find a route through before Dow clipped the ball on to the top of the bar with a right-footed effort from the edge of the area.
United forced a series of corners late on and Gavin Gunning's back-post header from Willo Flood's set-piece was parried clear by Fraser. Fraser then saved from Watson as United were again frustrated and County survived.