Victory over Croatian champions Medvescak Zagreb arrived off an impressive display on the opening night of three consecutive appearances at The SSE Arena.
Tyler Beskorowany posted a shutout - turning away 34 shots - with goals from Jim Vandermeer, Lewis Hook, Dustin Johner and Pat Dwyer helping the Giants to a win.
The Giants win sees the Belfast side sit joint top of the semi-final group, following GKS Katowice of Poland’s earlier 4-0 win against Ritten of Italy.
Netminders Beskorowany and Vilim Rosandic shut the door for the majority of the opening period.
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However, it would be the hosts who took a late lead in the city meeting.
Dwyer’s clever play saw the forward pick out an onrushing Vandermeer, who finished well into the Medvescak net with only 15 seconds left on the clock.
The Giants picked up where they left off in the middle period and doubled their lead early in the second.
Dwyer was, again, the provider and this time fed the puck to Hook to cooly slot home past Rosandic.
Johner opened his Continental Cup account at 49:24, pulling a classy move on the Medvescak netminder, assisted by Hunter Bishop.
Dwyer capped a magnificent performance with a goal of his own, rounding off the Giants scoring at 58:45, assisted by Kyle Baun.
Missing for the Belfast side were Colin Shields, Jonathan Ferland, Matt Towe, Andrew Dickson, Guillaume Gelinas and Francis Beauvillier.
The Giants will turnaround quickly as they face Italy’s Ritten Sport on Friday with a face-off at 7 o’clock.
Friday’s early game sees Medvescak Zagreb take on GKS Katowice at 3 o’clock.
Belfast Giants’ final group game comes on Saturday against GKS Katowice, with face-off 7 o’clock following the clash of Ritten Sport and Medvescak Zagreb.