Nick Ross gave Caley the lead in the ninth minute but Neil Lennon's side leveled after 20 minutes through Kris Commons with a superb effort.
Debutant Rami Gershon then headed the Hoops in-front, before Miku grabbed a third in the 82nd minute.
Tuesday night's opponents Juventus ran out 2-0 winners over Fiorentina on Saturday with first-half goals from Mirko Vucinic and Alessandro Matri.
The Bianconeri knew that failure to beat Fiorentina would have heaped pressure at the top of the table with Napoli facing Lazio but Antonio Conte's side stood strong.
Vucinic was left unchallenged to put the Old Lady in front before Matri scored one of he strangest goals you will see as the Italian's boot came off in the build up, only for him to volley home in just his sock.
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