Second-half goals from Jamie Smith and Graham Bayne gave the SPL's two most northerly clubs a point apiece, a result that neither side could argue with.
The visitors were the first to show, a Stevie Crawford header from a Scott Muirhead cross flashing just over in six minutes. Shortly after, Kevin McNaughton was unlucky when he cut in from the right before firing a dipping left-foot shot that went narrowly wide.
After 17 minutes a Jamie Smith free-kick was headed goalwards by Scott Severin but Mark Brown was on hand to save. Sixty seconds later Smith should have done better than a left foot strike that went well wide from 15 yards.
Inverness were rarely seen as an attacking force, but in the 28th minute a mis-hit from Dennis Wyness saw Craig Dargo flick the ball audaciously over his head straight into the arms of Ryan Esson.
A minute after the re-start Liam Fox attempted a speculative shot from distance that shaved the outside of Esson's right post.
In the 54th minute the visitors took the lead and what a beauty it was! Crawford found Gary Dempsey, who in turn passed to Jamie Smith. With several team-mates screaming for the ball, the former Celt looked up before firing a thunderous effort from fully 30 yards that left Brown helpless.
Caley brought on Graham Bayne for his first game of the season replacing Dargo, and in the 69th minute an Alan Morgan drive from distance wasn't far away after the Dons had only half cleared a corner.
Three minutes later Inverness levelled when Esson could only parry a fierce David Proctor shot. The ball fell to Bayne, who gleefully fired high into the net.
The home side had the chance to snatch the winner right at the death with only a last-gasp Russell Anderson tackle denying substitute Richard Hart.