Goals from Aaron Doran and Graeme Shinnie in the early stages of either half earned the win, with Darren Barr scoring a late consolation for Killie.
Caley Thistle struck after just seven minutes when Billy McKay got on the end of a Marley Watkins cross and laid the ball into the path of Doran to beat the keeper with a deflected shot off Sean Clohessy.
And the hosts could have scored a second when Ross Draper crashed a drive over the bar after more good work from Watkins.
But Killie had chances either side of that with Kris Boys fizzing a drive just over, before hesitation from Michael Gardyne inside the box allowed Richie Foran to nick the ball shortly before the break.
Inverness doubled their lead seven minutes after the interval when a flowing move ended with Foran releasing Shinnie, who cut past Barr and curled a superb effort past Craig Samson.
Kilmarnock gave themselves a lifeline when Barr (76) lost his marker to turn home an inswinging free-kick from substitute Sammy Clingan.
But Killie were unable to create in the remainder of the game, and were fortunate not to lose a third goal when a Nick Ross header came off the upright in the dying minutes.