The Dons revival under manager Craig Brown continued with youngster Ryan Jack rocketing home his first goal for the club with a 25-yard thunderbolt in the 44th minute.
And Nick Blackman wrapped up the victory on 48 when his close-range effort was deflected past keeper Ryan Esson.
Inverness were at a disadvantage for most of the game after central defender Grant Munro was dismissed for an off-the-ball incident after 18 minutes.
Influential Irish midfielder Jonny Hayes started for Inverness after being sidelined with an ankle injury for a month.
The talented playmaker showed glimpses of what he could offer when he returned for 15 minutes in the 1-1 draw at home to Hamilton Accies at the weekend and was preferred here to Eric Odhiambo.
Meanwhile, 18-year-old Jack was included ahead of Derek Young in the only change to the Aberdeen starting line-up from the side who lost 1-0 at Celtic on Saturday.
Aberdeen started brightly with Robert Milsom testing Esson in the opening seconds with a low shot from just outside the box.
The hosts responded well with Chris Innes powering a header on target from a Hayes corner moments later.
Blackman might have broken the deadlock in the 13th minute when he latched onto a long clearance but the Dons frontman sent his angled shot wide of the mark.
Even closer was Zander Diamond seconds later when his header from a Milsom corner hit the post.
Inverness were reduced to 10 men after 18 minutes when Munro was shown red.
The central defender was dismissed for an off-the-ball incident by referee Steve Conroy after he discussed the matter with his assistant.
Inverness manager Terry Butcher shuffled his pack to deal with the setback by switching full-back Ross Tokely to centre-half and dropping midfielder Stuart Duff into defence.
Blackman was next in the referee's notebook when he was shown yellow for a reckless challenge on Hayes, with the home fans calling for the whistler to even up the numbers.
The demands were repeated moments later when Rory McArdle lunged at Graeme Shinnie, leaving the Inverness youngster needing treatment while the Dons full-back was booked.
Inverness midfielder Dani Sanchez carved out an opportunity for top scorer Adam Rooney, but the striker failed to connect with the chance.
The visitors hit back in sensational fashion when Jack scored his wonder strike.
Blackman doubled Aberdeen's lead three minutes into the second half when his deflected shot found the net in front of the visiting fans. It appeared as if Caley Thistle defender Tokely got the last touch on the eight-yard shot.
Moments earlier Rooney squandered a glorious chance for an equaliser when he lashed an effort over the bar from around 10 yards after being found by Shinnie.
Chris Maguire would have added to Aberdeen's advantage just before the hour but for Esson, who stopped his bullet header from Milsom's corner.
Aberdeen were in the ascendancy and Blackman was next to be deprived by Esson when he was one-on-one after being played in by Dons captain Paul Hartley.
Esson was almost becoming a one-man barrier and stopped Maguire's shot from the edge of the area when the ball was laid back by Scott Vernon.
Hayes appeared to take a knock to his knee and was soon replaced by Odhiambo with just over 15 minutes to go as Inverness searched for a comeback.
It seemed to add a spark to the hosts with a couple of chances falling to Rooney, but his dry spell in the SPL continued.
The barren run, which stretches back to mid-November, looked likely to end with 10 minutes remaining when Rooney rounded keeper Jamie Langfield but Diamond cleared off the line.
On-loan Blackburn winger Aaron Doran was introduced with eight minutes to go and showed promising signs, but it was little consolation for the Highlanders whose two-month league winless run was extended while resurgent Aberdeen roll on.
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