Yoann Arquin’s first half header for the visitors was cancelled out by Marley Watkins after the break.
However, the stars of the show were goalkeepers Dean Brill and Mark Brown who limited an exciting contest to just two goals.
County controlled the opening 45 minutes while Caley Thistle were equally as dominant in the second half.
Rocco Quinn missed a great chance to open the scoring after just three minutes, sidefooting wide of the left post from 12 yards.
As the visitors continued to press, Graham Carey flashed a 24-yard free-kick over the bar.
County were presented with another excellent opportunity in the 16th minute when Filip Kiss pounced on a weak back-pass by Ross Draper but he was unable to slip the ball beyond advancing keeper Brill.
Bottom-of-the-table County took a deserved lead in the 21st minute when Arquin nodded home Quinn’s looping cross.
County remained the dominant team and Brill made a number of excellent saves to prevent their highland neighbours from extending their advantage before the break.
First, Quinn fired straight at the keeper when in space 10 yards out before Arquin was also denied less than 60 seconds later and, on the brink of half-time, Brill dived to push away a curling Carey free-kick.
At the other end Brown had to be alert to keep out Ryan Christie on a rare Inverness attack towards the end of the first half.
But while County reigned before the break, the second half was all about the hosts.
With less than four minutes played Inverness had levelled when Watkins slipped the ball home from close range after latching on to Christie’s low cross.
Keeper Brown came to County’s rescue on 68 blocking a Watkins effort from six yards and six minutes later Billy Mackay scuffed a good chance wide of the left post as he raced into the box.
And Brown came to County’s rescue twice more during the final 10 minutes. First, he brilliantly saved from Mackay before blocking a firm strike by Draper, as County held on for a point.