Inverness continued to press forward and double their lead 20 minutes later when Andrew Shinnie escaped the defenders to finish in the bottom corner.
County had a couple of counter-attacking opportunities but could not find a goal before half-time.
They found one soon after the break though. Three minutes into the second half, Iain Vigurs scored a fantastic free kick to get the away side back in the game.
Ross County could not find an equaliser and it was the home team who scored next to put the result beyond doubt.
With three minutes left a nice passing move found Aaron Doran free on the edge of the box. The midfielder finished well to make it 3-1.