Inverness had not played a competitive match this year following the winter break, but showed little sign of any rustiness as a ruthless second-half display saw them emphatically dispatch the Dons.
A spectacular 54th-minute opener from Andrew Shinnie was followed up by two Billy McKay goals, taking his tally for Caley Thistle this season to 20.
The win made it 10 games unbeaten for Inverness in all competitions and just one defeat in their previous 21 outings ahead of the club's first appearance in the last four of the League Cup when they take on Hearts at Easter Road this weekend.
Caley Thistle boss Butcher said: "It's never easy against Aberdeen, especially as they have players like Jonny Hayes, Niall McGinn and Josh Magennis, who can hit you on the break.
"They put us under pressure at times, but I always felt we could get a goal on the break as well.
"Once we managed to get our noses in front you could see the confidence flowing through the players.
"It was great to come back from the break with a win and now we've got the semi-final of the League Cup to play this weekend, so we'll look forward to that."
Aberdeen missed the opportunity to close the gap on second-placed Inverness and remain in fifth position in the Scottish Premier League.
For Dons manager Craig Brown, however, the result could have been different if his side had taken the lead.
He said: "If you analyse the possession and the chances created by either side then you'll probably find that the game was quite even.
"Had we got the first goal then it may have been different, but we didn't.
"However, all credit to Terry Butcher and his players. We were not as clinical as they were."