A David Raven own goal (69) and Niall McGinn’s (74) close-range finish sealed the fightback after Edward Ofere’s opener for the home side, who remain third, four points clear of St Johnstone.
Marley Watkins had the first chance of a poor opening 45 minutes when he latched onto Nick Ross’ through-ball, but Dons keeper Scott Brown was out quickly to smother the attempt.
With both sides struggling to create, Aberdeen saw Adam Rooney skew wide under pressure before McGinn drilled straight at Ryan Esson.
Ross then shot straight at Brown after being played in by Ryan Christie and Watkins was equally guilty with an even better chance six yards out – his connection not good enough to beat a sprawling Brown.
The Inverness striker then blazed over after good work from Josh Meekings before the home side finally had their reward four minutes into the second-half – Ofere scooping the ball into the net after his initial header had been saved from Watkins’ cross.
Undeterred, the visitors hit back with Ryan Jack drawing a fine save from Esson before a goalmouth scramble had the Dons appealing in vain for a handball.
They were level with 20 minutes to go though as McGinn’s in-swinging free-kick glanced off the head of Raven and crept inside Esson’s far post.
And Aberdeen were swiftly in front. Jonny Hayes’ corner found Rooney, whose effort was blocked on the line by Gary Warren but McGinn was on hand to turn in the rebound.
Despite late huffing and puffing, Inverness were unable to break down a stubborn Aberdeen rearguard again as the visitors completed a clean sweep over their opponents.