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.
However, for the Parkhead club, this game was less about cementing their place at the top of the table and more about the first leg of their Champions League last-16 clash with Juventus at Parkhead on Tuesday night.
As promised, Neil Lennon rang the changes although number one keeper Fraser Forster was back after recovering from a neck injury and handed the captaincy in the absence of Scott Brown.
Gershon, on loan until the end of the season from Standard Liege, and Australian midfielder Tom Rogic, who signed from Central Coast Mariners, were two of nine changes to the side that beat Raith Rovers in the William Hill Scottish Cup last week. Defender Marcus Fraser started in the SPL for the first time while there were rare starts for Paddy McCourt, Dylan McGeouch and Miku.
Caley showed one change with midfielder Ross Draper in for Richie Foran, who was not even in the squad, and it was Terry Butcher’s men who went ahead in the ninth minute.
Aaron Doran’s dangerous right-footed cross from the left appeared to be kneed away by 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 Rogic showed why 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.
Joe Chalmers replaced Commons for the start of the second half, emphasising again the importance Lennon was giving to the visit of Juventus, and the Celtic boss was delighted to see his side go ahead three minutes after the break.
Israeli centre-half Gershon rose inside a packed Caley box to power a header past the helpless Ryan Esson from McGeouch’s flighted cross.
Stokes headed a McGeouch corner against the bar before Caley began to exert some pressure, with substitute Adam Matthews having to clear a shot from Billy McKay off the line.
However, with eight minutes remaining Caley found themselves further behind as they pushed up the park, allowing Stokes to play in Miku, who slotted past Esson from eight yards.