Hamilton started the match in style when Scotland finished from close range inside the opening two minutes.
A Ross County corner caused problems for the Accies defence five minutes later, but Scott Boyd shot over the bar from six yards.
Imrie doubled Hamilton's lead in the 17th minute, directing the ball into the top-right corner of the net after Ali Crawford put the striker through one-on-one.
Michael Gardyne failed to pull a goal back eight minutes later when his shot missed the left post.
County did pull a goal back in the 28th minute, though, as Curran headed into the net from close range after Raffaele de Vita's cross.
A good chance for Accies to regain their two-goal cushion fell to Daniel Redmond, but he shot wide from the edge of the penalty area.
Jake Jervis should have equalised for County on the verge of half-time, but his header went narrowly wide of the target.