Jason Scotland scored the opener after just two minutes as he knocked the ball home from close range to convert a Daniel Redmond corner after Ali Crawford had seen his shot saved by Ross goalkeeper Mark Brown.
The away side spurned the opportunity to draw level soon afterwards, Scott Boyd firing over from six yards after the loose ball had ricocheted around the penalty area.
Crawford continued to cause problems as Hamilton grew in confidence as his counter-attack from a County corner helped create the second goal.
The midfielder raced forwards before sending Dougie Imrie clean through and he calmly slotted the ball past Brown on 18 minutes.
The visitors bounced back though, with Craig Curran heading home after getting on the end of Raffaele De Vita’s cross to reduce the deficit to 2-1.
Redmond could have restored Hamilton’s two-goal lead but he shot wide from the edge of the area, with Jake Jervis then heading Martin Woods’ cross wide at the other end when he should have scored.
The game continued to be a lively affair after the restart, with Crawford firing a shot across goal and Curran saw a header cleared for Ross.
Hamilton continued to press, with Grant Gillespie clearing in his own goalmouth, before hitting the side netting at the other end.
County stuck to their task, however, and were rewarded with an equaliser after 72 minutes, with De Vita again providing the vital cross as Michael Gardyne finished neatly at the back post.
Both sides pushed for a winner in a frenetic end to the game but to no avail, with Hamilton player-manager Martin Canning’s winless run since taking over at New Douglas Park now extended to 10 matches.