On a day when both managers would have been unhappy with defensive lapses, Josh Meekings and Marley Watkins were on target for the visitors with Adam Rooney, Shaleum Logan and Jonny Hayes scoring the Aberdeen goals.
High-flying Caley Thistle opened the scoring on 16 minutes when Greg Tansey sent a free-kick into the box and Meekings lost his marker to power a header into the corner of the net - his first goal for Caley.
Aberdeen levelled nine minutes later when Gary Warren misjudged a header back to Dean Brill and Rooney latched on to the ball before rounding the keeper and slotting home.
The Dons took the lead for the first time five minutes before the break when Hayes got to the goal-line and cut-back a pass to David Goodwillie, and although the striker was unable to get in a shot he laid the ball off the Logan to drive his effort into the top corner.
Logan suffered a reverse in fortunes five minutes after the break when his attempted clearance went straight to Watkins inside the box and the Caley Thistle midfielder showed great composure to flick the ball past Jamie Langfield and roll it over the line.
And another defensive mistake, this time from Ross Draper, allowed Aberdeen to score their third when Goodwillie pounced on a sloppy pass, and although Brill parried his shot Hayes (59) was following up to net the rebound.
Two minutes after falling behind Aberdeen squandered a chance when Meekings got caught under a cross and Goodwillie chested the ball down but drove his shot straight at keeper Brill.
And Warren almost atoned for his error within 60 seconds when he found space at a corner and headed against the upright with Langfield rooted to his goal-line.