Having passed up numerous chances ICT finally got their noses in front in the 86th minute only to be pegged back with the last kick of the ball when a lapse in concentration allowed sub Steve Lovell to net an unlikely equaliser.
The first action of the game, a snapshot by Barry Nicholson from the edge of the area flew high over the crossbar.
On 12 minutes, a neat John Rankin pass slotted the ball behind the Dons rearguard allowing Roy McBain to drive into the box, before chipping up a delightful ball to the far post where Russell Anderson did well to head clear under severe pressure from Graham Bayne.
Minutes later, a clever sidestep by Dennis Wyness took him away from his marker before crashing in a fierce shot from 22 yards which was held at the second attempt by Jamie Langfield.
The visitors threatened again when Wyness knocked the ball wide to Barry Wilson who drove at Richard Foster before firing in a tremendous shot which Langfield did very well to parry wide at the expense of a corner.
Minutes later, Lee Miller slotted home from a Craig Brewster flick-on only for the goal to be chalked off for offside.
With 39 minutes gone, Anderson was penalised for going in late on Bayne. From the free-kick Wilson got the ball up and over the wall but also over the crossbar as the visitors continued to press.
Aberdeen were dealt a serious blow in 44 minutes when Brewster had to leave the field with a dislocated shoulder.
The Dons had a huge let-off at 66 minutes when a Rankin corner was turned back across the area by Darren Dods to the feet of Bayne, who, from eight yards, wildly shot over with the goal at his mercy.
Aberdeen passed up their best chance of the match thus far in 69 minutes. Michael Hart's long ball out of defence sent Daren Mackie scampering clear of his marker wide on the right, the forward held the ball up long enough to pick out Miller whose first-time effort from 18 yards screwed just over the crossbar.
As the game entered the final stages Inverness scored the goal which their play had thoroughly deserved.
The home defence failed to clear a Grant Munro throw into the area with the ball finally falling to Rankin, who slid the ball home to the obvious delight of the small band of visiting supporters.
However, there was a sting in the tale. Just when they thought they were going to pick up a much-needed victory, their hard work and endeavour was undone in the second minute of stoppage time.
Russell Duncan needlessly gave away possession in midfield, with Chris Clark intervening his wayward pass. With the ICT defence pushing out, the midfielder chipped the ball in to Lovell, who lofted the ball over the advancing Mark Brown to bring the sides level.