Delighted David Hopkin praised his Ayr side for digging deep to save their Championship skins in the Highlands.
United twice came from behind to secure the point they needed to avoid the relegation play-offs.
Josh Todd was the hero midway through the second half as his goal sealed the 2-2 draw that keeps Ayr in the league.
And Hopkin said: "Every man tonight played a part in this.
"Two weeks ago everyone thought we were dead and buried.
"But I wasn't going to let that happen.
"After the Arbroath game I worked on shape constantly and tonight you saw the performance of a team who wanted to stay in the Championship.
"We faced adversity twice, came back and showed character.
"I have fantastic footballers here but what pleased me most tonight was the way they dug in.
"I asked the likes of Luke McCowan, Michael Moffat and Joe Chalmers to do that.
"Josh Todd was the best player on the park.
"As a group over the last two weeks we have worked so hard and achieved what I set out to do when I came in - and that's stay in the Championship.
"I'm delighted for the chairman and the board who've given me the chance to come in here and the players who've bought into my ideas and philosophy.
"Hopefully we can now get some players in to complement what we have and start to push on."
Ayr had endured the nightmare start when Dan McKay fired Caley in front after just six minutes.
But they slowly grew into the game and hit back before the break when Aaron Muirhead slammed home a penalty after Jack Baird had gone to ground.
However, they were behind just seconds after the restart when Caley were awarded a spot kick of their own and Sean Welsh stepped up to convert.
But then came the vital moment as Baird flicked on a Chalmers ball into the path of Todd, who slammed home at the backpost.
Ayr then endured a nervy final 23 minutes but saw the game out to preserve their spot in the Championship.
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