Teenager Cammy Smith's first Aberdeen goal denied Inverness their maiden league win of the season.
Both sides scored after being reduced to 10 men, Caley Thistle losing Owain Tudur Jones for a strong challenge after 55 minutes.
Shane Sutherland was pulled down inside the penalty box 10 minutes later and Richie Foran scored from the spot-kick.
Dons captain Russell Anderson was sent off for his foul, but substitute Smith headed the equaliser after 84 minutes.
Aberdeen had arrived as the shut-out kings of the Scottish Premier League, Caley Thistle had the leakiest defence.
So both managers will take some satisfaction from the result and improved second-half displays, no doubt on the back of some strong words at the interval from Messrs Terry Butcher and Craig Brown.
Inverness gave a debut to on-loan Celtic defender Andre Blackman and the Englishman made an immediate impact with a heavy challenge on winger Ryan Fraser that ought to have had referee George Salmond reaching for at least a yellow card.
The Inverness faces were being battered by the strong sea breeze, but they were handing out a beating to the Dons wingers and Aaron Doran found himself presented with a booking after a foul on the man he has replaced in the starting line-up, Johnny Hayes.
That strong wind ensured that the Dons had the territorial advantage for much of the first half.
However, other than a few wind-assisted crosses, home goalkeeper Ryan Esson had little to deal with, although Ryan Jack and Stephen Hughes had efforts deflected just wide.
Yet Caley Thistle had the better chances to squander and Foran did just that, twice delaying the trigger too long in front of goal.
The second-half exploded into life as Dons defender Andrew Considine had a half-volley cleared off the line following a corner then Blackman sent a blistering, wind-assisted drive from 25 yards just wide.
Caley Thistle were down to 10 men when the towering Tudur Jones slid in powerfully to leave the diminutive Fraser crumpled in a heap.
It seemed a slightly harsh decision, but referee Salmond might have been influenced by the tough treatment being meted out by the home side - Josh Meekings had also been shown yellow in the first half.
Butcher re-arranged his chess pieces, with Foran dropping back into midfield and Andrew Shinnie being sacrificed.
Substitute Sutherland made an immediate impact playing on his own up front, his pace taking him behind the visiting defence and being felled by Anderson.
With the red-carded former Scotland defender on his way to the dressing-room, Foran sent goalkeeper Jamie Langfield the wrong way from the spot.
Caley Thistle should have wrapped up the points when Foran found Doran in front of goal on the break, but the winger delayed too long and Mark Reynolds' tackle saved the day for the Dons.
The home side paid for that when Hayes' cross was despatched by Smith and there was further disappointment when Sutherland was stretchered off in stoppage time.