Kyle continued his excellent scoring form for Kilmarnock
Inverness remain in danger of relegation after Kevin Kyle's header ensured SPL safety for Kilmarnock.
The visitors made a bright start, with Richie Foran, Brian Kerr and Filipe Morais all threatening.
Kyle went close with a header from on the stroke of half time but his effort was hacked clear off the line.
However, the big former Scotland striker was not to be denied and found the target from close range after good work from Garry Hay on 78 minutes.
Inverness must now avoid defeat at home to bottom club Falkirk next weekend to stay in the top flight.
With a draw suiting both sides, it was no surprise that this was not much of a contest, although the Highlanders played the more adventurous football.
Foran was close to connecting with a dangerous ball across the face of the goal by Roy McBain and Brian Kerr saw his deflected shot drift just wide of the target.
Fifteen minutes before the break, Filipe Morais caught the home defence napping on the counter-attack but fired just wide.
With less than a minute left of the first half, Kilmarnock finally posed a threat and Kyle's header from eight yards was cleared off the line.
Inverness left-back Lionel Djebi-Zadi fired into the side-netting five minutes after the interval, while Morais saw his shot was easily saved by Combe after eluding the home defence.
Djebi-Zadi tried his luck again from distance, but Combe held the effort without any trouble.
As Inverness tired, the home side started to find Kyle more often with their favoured route of the long ball
And, with 12 minutes remaining, Mehdi Taouil beat his man and supplied Hay, who crossed for Kyle to knock the ball home at the back post.
Moroccan playmaker Taouil nearly made in 2-0 in the last minute but his effort hit the post.
Kilmarnock manager Jim Jefferies:
"There were a lot of nerves today and Inverness have been stuffy opponents for us this season.
"We were much better in the second half and we could've killed them off when they were pushing forward.
"Getting seven points from the last nine has been a fabulous achievement. We knew with three games at home that it was in our own hands.
"Last year we were 11th, so we've improved. All the players have worked hard as they knew this season was going to be tight.
"Five teams being involved in relegation doesn't happen very often."
Inverness manager Terry Butcher:
"The players put in another great shift but it just wasn't to be. You're asking the same players to play three games within a week.
"The one fixture that matters now is the one at home next week. So we've still got an opportunity.
"We dominated the first half and I thought we deserved to go in ahead, but it wasn't to be.
"Kilmarnock then pegged us back. But it's still in our own hands and if we avoid defeat next week against Falkirk then we stay up.
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