Targets from Austin Samuel and on-loan Hibs starlet Daniel MacKay gave the Highlanders a 2-0 cushion.
Lions keeper Max Stryek was red-carded for a disputed last-man problem on Samuels with ICT one purpose in entrance.
First-team coach Barry Wilson reckons Caley Thistle deserve reward for standing sturdy for his or her 2-1 Premier Sports activities Cup win at Premiership Livingston.
Jason Holt pulled one again for the hosts earlier than then lacking a late spot-kick as Inverness went again up the A9 with two wins from two and high of Group G.
Cove and Kelty have simply performed as soon as, however Billy Dodds’ staff now have management of the part with two fixtures left.
Coach Wilson praised his gamers for digging deep to carry on beneath large strain from their Premiership opponents.
He mentioned: “We’re clearly delighted to win right here. We didn’t begin very properly. We couldn’t maintain maintain of the ball and Livingston induced us loads of issues with their little formations in the midst of the park.
“As soon as we obtained maintain of the ball, we have been superb. As soon as we get forward and are a person up, we began dropping deeper and deeper which meant our additional man wasn’t counting.
“Truthful play to Livi as they gave the whole lot and the penalty on the finish was an enormous turning level. We obtained a break from it and we take three factors and go up the highway.”
Wilson was thrilled with the talent of Daniel MacKay, who’s again on mortgage from Hibs, but in addition warned nothing is determined after two group video games.
He added: “Daniel was again to exhibiting what we all know he can do, being direct and with tempo. He induced them loads of issues.
“Their purpose modified the whole lot. They obtained their tails up and we obtained nervy.
“It’s an enormous outcome for us. This competitors is huge for us and it’s been 5 or 6 years since we progressed.
“It’s huge when it comes to the monetary side and the momentum it offers you going into the beginning of the league season. There’s nothing worse than being out of the cup earlier than the season begins.
“We now have two residence video games and now we have six factors. We’re in a great place, however nonetheless with work to do.”