Killie, still searching for their first SPL victory in 2009, made the brighter start and could have taken the lead inside the first minute when Jamie Hamill released Craig Bryson, but Ryan Esson was out quickly to save with his feet.
The visitors continued to apply the pressure and Danny Invincibile really should have done better after being put clean through by Kevin Kyle's flick on, yet he dallied on the ball and that allowed Ross Tokely to get back and make a timely intervention.
Caley Thistle had rarely threatened Kilmarnock's goal, but they took the lead on 19 minutes as Richie Foran out-jumped goalkeeper Alan Combe to head home Tokely's hopeful ball into the box.
It proceeded to get even better for Inverness three minutes later when Ian Black's bending free-kick eluded the heads of both Pavels Mihadjuks and Tokely, although it mattered little as an unsighted Combe could not prevent the ball from nestling into the corner of the net.
This seemed to knock the stuffing out of Jim Jefferies' men, but they breathed new life into the contest in stoppage time at the end of the first half.
The hosts could not clear a couple of corners and as the ball eventually fell to Garry Hay, he picked out the unmarked Simon Ford, who powerfully headed past a motionless Esson.
As in the first half, Killie were on the ascendancy immediately after the interval and Esson did well to turn away Gavin Skelton's volley from the edge of the box.
Both teams then struggled in the blustery conditions and neither goalkeeper was seriously tested for much of the second period.
Kilmarnock did attempt to apply late pressure, but Caley Thistle held firm to move to within a point of the Ayrshire side.