The visitors had the better of the scoring opportunities particularly in the second half, but found Aberdeen keeper Jamie Langfield on top form.
In a bright start by the home side, Aberdeen created several good opportunities in the opening ten minutes.
The first of these on seven minutes saw Chris Clark release Sone Aluko, who drove to the byline where he picked out Jamie Smith with his cut-back, but the striker hesitated and was eventually crowded out.
In the following minute, visiting skipper Grant Munro totally misjudged a long clearance from the Aberdeen defence, allowing Jamie Smith to drive at the goal where he tried an audacious lob from 35 yards which Michael Fraser cleared after scrambling back.
Aberdeen continued to press and on 21 minutes Derek Young drove down the right before pulling back a great cross to the far post which Lee Miller only just failed to head home under pressure from Munro.
On 45 minutes, a swift counter-attack saw Richie Byrne push the ball wide to Richard Foster, who advanced before releasing Aluko with a brilliant ball.
The wideman's pace took him beyond his marker but his low driven ball flew across goal only to be narrowly missed by the on-rushing Jamie Smith.
At the other end, a dangerous Russell Duncan free-kick found the head of a Ross Tokely, who climbed well above his marker but couldn't keep his header on target.
The visitors continued to hit Aberdeen on the counter-attack and from a Tokely cross the ball was played back into the path of Ian Black by Graham Bayne.
The diminutive midfielder's first-time effort from 28 yards was flying into the top corner, only for an acrobatic save from Langfield to keep his side on level terms.
On 66 minutes, hesitation between Aberdeen centre-backs Lee Mair and RByrne almost gifted Caley Thistle the lead, but Langfield got down brilliantly at his left-hand post to save a Marius Niculae 14-yard snap-shot.
On 75 minutes, John Rankin's deep cross fell on to the head of Black, but with the goal at his mercy he nodded meekly wide.
With the game heading for a stalemate, Aberdeen took the lead on 83 minutes.
Miller drove at the defence only to be unceremoniously bundled over by Tokely inside the area.
Referee Mike Tumilty correctly awarded a spot-kick which saw Barry Nicholson expertly send keeper Fraser the wrong way to open the scoring and settle the match.