Tyler Beskorowany kept a blank for the second game in Belfast’s last three as Adam Keefe’s side showed they meant business in this opening game.
The Giants took the lead with 15 seconds of the first period remaining when Jim Vandermeer was picked out by Pat Dwyer as he sent the puck into the net.
Dwyer doubled his points tally as Lewis Hook was the beneficiary, finishing one off past Zagreb goalie Vilim Rosandic .
It was three without reply in the third period as Dustin Johner got on the scoresheet with around ten minutes to go before Dwyer rounded a good night’s work off with the fourth late on.
In the day’s other game, GKS Katowice got their campaign off to a similarly impressive start as they hit Italian side Ritten Sport with the same scoreline.
Tomasz Malasinski got two, with one apiece for Jesse Rohtla and Janne Laakkonen to take them into the second day in the best possible spirits.
Katowice will face Zagreb in the day’s early game (3pm) before Belfast take to the ice against Ritten Sport at 7pm in their second match.