Nick Ross gave Caley the lead in the ninth minute only for Hoops midfielder Kris Commons to level in the 20th minute with the sweetest of left-footed strikes.
Three minutes into the second half debutant Rami Gershon headed the champions into the lead before Miku grabbed a third in the 82nd minute as the visitors ran out easy winners.
After just nine minutes of play, Terry Butcher's men went ahead. Aaron Doran's dangerous right-footed cross from the left appeared to be kneed away by Fraser Forster but only as far as Ross at the edge of the box who, with green and white shirts slow to close him down, fired it back into the corner of the net.
The goal stung Celtic into action and it was Tom Rogic who showed why manager Neil Lennon was so keen to bring him over from Australia in January.
The midfielder drove into the right side of box, skipping past Owain Tudur Jones with ease, and when his cutback arrived at Commons on the far side, the Scotland midfielder rifled it high past Ryan Esson from 14 yards.
There was a penalty shout moments after the restart when Doran's cross from the right was blocked by Marcus Fraser but referee Craig Thomson pointed for a corner kick and the Parkhead men easily cleared their lines.
Gershon's goal in the 48th minute was simple enough. The Israeli stopper rose inside a packed Caley box to power a header past the helpless Esson from Dylan McGeouch's flighted cross and suddenly Inverness looked shot of confidence.
In the 71st minute, as the ball pinballed around the Celtic penalty area, Hoops substitute Adam Matthews, on for Gershon, was on hand to clear a shot from Billy McKay off the line as the Parkhead side wobbled. However, with eight minutes remaining Caley found themselves further behind as they pushed up the park.
Tony Watt, on for Patrick McCourt, sent Anthony Stokes free on a counter-attack and when the former Hibernian striker played in Miku he slotted it past Esson from eight yards and there was still time for the Venezuelan then hit the post from a Matthews cross.