The visitors conceded two spot-kicks and a howler from keeper Mike Fraser put the quarter-final tie beyond Craig Brewster's side within the first 45 minutes.
Aberdeen were without their skipper Scott Severin who was a late withdrawal due to injury so Michael Hart was captain for the night.
Despite early pressure from the visitors, Aberdeen took the lead with their first meaningful attack in the tenth minute.
Neat interplay between Jamie Smith and Derek Young saw the latter needlessly scythed to the floor leaving referee John Underhill no option but to award a spot-kick.
Barry Nicholson made an immaculate job of driving the resulting penalty into the right-hand corner of the net.
Aberdeen pressed again minutes later when Nicholson's free-kick was met at the near post by Young whose header flashed just over with Caley keeper Fraser stranded.
From a deep Don Cowie free-kick on 14 minutes, the ball fell onto the head of Aberdeen's Ross Tokely whose effort flew narrowly wide when under pressure from Richie Byrne.
Sone Aluko, Smith and Lee Miller were running riot for the home side with their vision and pace and it came as no surprise when they extended their lead on 21 minutes.
Miller's forceful run carried him into the visitors area where he was unceremoniously barged over by Richard Hastings to give the Dons another penalty.
Nicholson's spot-kick mirrored his first effort as it flew just inside the right upright.
Casual play by Aberdeen twice nearly let the visitors back into the match with Jamie Langfield having to look particularly lively to turn a fierce 25-yard Cowie effort round the post in the 39th minute.
Disaster struck for the visitors on the stroke of half-time when Grant Munro played the ball back to his keeper. Fraser controlled the ball on his chest before losing possession, allowing Miller to step in and easily prod the ball home from eight yards.
In the opening 15 minutes of the second half the only worthwhile effort on goal was Dennis Wyness' header from an accurate Tokely cross.
Wyness then flashed a couple of half-chances wide of the target as the visitors continued to press.
Inverness were thrown a lifeline on 68 minutes when Alexander Diamond had time to clear but tried to be too clever and was easily dispossessed by Wyness who crossed for Graham Bayne to sweep the ball home.
Aberdeen finally killed off any hope Inverness had of getting back into the match on 78 minutes.
A sweeping counter-attack saw Andrew Considine break from defence to find Chris Clark wide on the right.
He drove past Hastings before playing in a tremendous deep ball into the area which Nicholson stabbed home from seven yards out to complete his hat-trick.