Victory for either side at Tannadice would have seen them climb to the top of the SPL - at least until Saturday's fixtures - 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.
United and County have been familiar foes in cup competition in recent seasons, most notably in 2010 when Peter Houston's men prevailed 3-0 at Hampden to lift the Scottish Cup.
United were without captain Jon Daly following a knock sustained in the 0-0 draw against St Johnstone prior to the international break in a side showing three changes.
Midfielder Michael Gardyne was brought in for his second United start after his summer move from Dingwall, a deal agreed in January before he helped County clinch promotion.
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 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.
County went close early in the second half when an Iain Vigurs cross went marginally in front of McMenamin before Cierzniak scrambled to stop Gary Glen getting in a shot.
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.
Dow troubled the visitors once more on the left and crossed weakly. The ball hit Grant Munro on the right foot and was picked up by Fraser, with Collum dismissing the suggestion it was a deliberate pass-back.
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.
Rankin almost found an opening, but three County defenders snuffed out the chance, before United introduced 16-year-old forward Ryan Gauld in an effort to find the breakthrough.
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.
County's next match comes on September 22 against St Johnstone, by which time 400 days will have elapsed since their last league loss.