Inverness had the better of the early chances as Billy McKay found his way around several defenders inside the opening 20 minutes, but was unable to put the ball in.
The hosts did manage to find the back of the net when Yoann Arquin headed the ball forward for Yann Songo'o, but the midfielder was offside.
The visitors edged ahead just before the break when Aaron Doran caught out Mark Brown with a strike from inside his own half, just moments after the Ross County keeper had denied Greg Tansey from a free kick.
The visitors believed that they should have had a penalty just before the hour mark when Marley Watkins went down in the penalty area, but the referee was not interested in their appeals.
Inverness regained the lead with just over 10 minutes left to play as McKay picked up the ball in the box, initially having his effort blocked, but was able to react quickly to put the rebound in.
Graeme Shinnie almost put the result beyond doubt with a low strike in the final two minutes, while McKay struck the bar looking for his second in stoppage time.