Novak opened up the scoring within the first 10 minutes of the game as Gray laid off the ball for Novak, who picked out the top right-hand corner from 20 yards out.
The favour was returned not long after as it was Novak's turn to assist. He worked the ball from the left, leaving Gray to finish from a tight angle to double their lead.
The Blues went into half time the better side but it was Inverness who came out the stronger in the second.
Inverness came close to equalising late on, but it was Birmingham who sealed the result with a late penalty scored by Caddis after Clayton Donaldson rounded the keeper and was brought down.
Birmingham held on for the remaining minutes to see off their Scottish opponents to win 3-1 at St Andrew's.