Inverness turned in an impressive first half display
Mehdi Taouil missed a late penalty for Kilmarnock as Inverness profited from an energetic approach and some sloppy defending to take maximum points.
Doug Imrie smashed in an early opener from close range and Garry Wood headed in the second as goalkeeper Alan Combe failed to gather a high cross.
Willie Gibson drilled home a fine strike to spark the Killie fightback.
The home side won a spot-kick on 89 minutes, but Taouil's terrible effort flew high over the crossbar.
The win pulls Inverness further away from the bottom of the table and closes the Highlanders to within two points of Kilmarnock.
Ian Black was booked for flattening Combe in the opening minutes and that set the tone for what was a bad tempered match, littered with fouls and hefty challenges.
But it was the visitors who were sharper in the tackle and carried more attacking menace, so it was no surprise when they took the lead on 14 minutes.
The home side allowed Don Cowie's deep cross from the left to reach the onrushing Imrie at the back post and the midfielder's shot slammed into the net via a deflection and the underside of the crossbar.
Kilmarnock manager Jim Jefferies must have been furious at the slipshod nature of the defending, but nothing could have prepared him for the shocking circumstances under which the second goal was gifted away.
Eight minutes before the interval, Cowie lofted a hopeful ball into the penalty box and Wood beat Combe to what looked a routine catch.
The ball simply bobbled off the top of the striker's head and bounced over the goal-line.
David Fernandez made a rare break forward for Killie, but his shot from 20 yards was comfortably gathered by Ryan Esson.
Taouil drove Kilmarnock on just before the interval and the little Moroccan came close with a cross from the left that saw Allan Russell inches away from connecting for a header right in front of goal.
Russell did get his head to a good Craig Bryson delivery early in the second half, but the striker's effort was blocked by defender David Proctor, who did not appear to know much about it.
Combe did not return for the second half and his replacement, Damien Rascle, made a terrific reaction save to keep out a close range header from Wood.
Not to be outdone, Esson matched his opposite number's acrobatics with a super effort to scoop away a sharp downward header from Manuel Pascali.
With Taouil at the heart of things, Killie did most of the pressing in the latter stages, but the visitors remained a threat on the break.
Substitute Andrew Barrowman slid a shot narrowly wide from 18 yards on one such counter-attack.
The same player had the ball in the back of the net on 80 minutes but was thwarted by a linesman's flag.
Kilmarnock pulled a goal back on 84 minutes when Gibson exchanged passes with Fernadez and drilled a shot beyond Esson from the edge of the penalty box.
Gibson was then clipped by Imrie to win a penalty, but Taouil sent his spot-kick into the crowd.
Kilmarnock manager Jim Jefferies:
"We weren't at the races in the first half. Inverness are a difficult team away from home; they get men behind the ball and it's difficult to find space and make things happen.
"We lost a bad second goal and had a mountain climb, but we pummelled them in the second half.
"We could have won it on second-half chances. Our passing was better, the tempo was better. It was night and day from the first half.
"I was a bit surprised Mehdi tried to go for power on the penalty rather than what he's good at; placing the ball.
"But penalties have been missed before and no-one will be more disappointed than Mehdi. We're all in it together, so we'll pick him up at get on with it."
Inverness manager Craig Brewster:
"We were superb in the first 45 minutes. Our passing was excellent, as was our work-rate without the ball.
"We knew Kilmarnock would put us under pressure after the break and Willie Gibson came on to cause us problems.
"We passed up a great chance to wrap up the points with a four versus two situation and they go up the park and win a penalty.
"It was just lady luck that he missed."
Kilmarnock: Combe (Rascle 46), Fowler, Wright, Ford (Simmonds 77), Hay, Hamill, Taouil, Bryson, Pascali, Fernandez, Russell (Gibson 59). Subs Not Used: Murray, Skelton, Flannigan, Cox. Booked: Hay, Wright, Fernandez, Hamill.
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