Goals from Ross Draper, Andrew Shinnie and Aaron Doran sent Inverness into the Scottish Premier League top six after an end-to-end encounter at the Tulloch Caledonian Stadium.
Draper's ninth minute close range header gave the hosts the lead before Andrew Shinnie's 12-yard effort after 28 minutes gave them a two-goal cushion at the interval.
Iain Vigurs' superb free-kick reduced arrears for County after 48 minutes, but Doran's volley with two minutes to go sealed the victory for Inverness.
The home side were boosted by the return of Welsh midfielder Owain Tudur Jones after a three-match ban.
Jones, who was sent off in both of his previous outings at Tulloch Caledonian Stadium this season, replaced Gavin Morrison in the only change to the side who beat Dundee United 4-0 last Saturday.
County captain Richard Brittain and striker Colin McMenamin came in for the visitors in place of Stuart Kettlewell and Sam Morrow following the Staggies' 5-4 loss at St Mirren last time out.
Former Inverness star Ross Tokely almost turned the ball past County team-mate keeper Michael Fraser when he headed an Aaron Doran cross onto the bar in the opening minute.
Seconds later ex-Inverness captain Grant Munro cleared the County lines when Jones sent a shot towards the far post.
Philip Roberts was next to break forward for the hosts and his low cross was steered just wide by Andrew Shinnie.
Inverness made the pressure count when Draper headed home a Graeme Shinnie corner from close range in the ninth minute.
County responded well with Mark Fortheringham hitting the woodwork from 25-yards and Brittain was next to come close for County when his 30-yard free-kick went just wide.
It proved costly as the hosts scored at the opposite end moments later. Richie Foran capitalised on a Munro error after 28 minutes and swiftly found Andrew Shinnie who fired low beyond Fraser from 12-yards.
Munro almost made amends when he headed a Brittain free-kick goalbound but his effort was thwarted by Inverness keeper Antonio Reguero.
Doran would have put the home side further ahead when he was played through by Roberts, but Fraser saved well with his feet.
County got themselves back in the game three minutes into the second half when Iain Vigurs curled a 25-yard free-kick into the top corner.
The visitors piled on the pressure in search of an equaliser as Inverness reverted to long-ball tactics.
Efforts from Marc Fitzpatrick and McMenamin went across the face of goal and Rocco Quinn forced a save from Reguero, before Vigurs came close to netting his second when his angled shot went inches past the post.
As County poured forward Inverness almost grabbed another when Draper met a low David Raven cross, but Fraser made the save.
Quinn might have levelled late on when he met a Fitzpatrick cross on the volley but Reguero was again equal to it.
However the hosts sealed the win when substitute Conor Pepper was provider as he found Doran whose hammered a stunning volley past Fraser with two minutes to go.