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Sheffield Steelers forward Robert Dowd scored the opening goal and added two assists as GB sealed victory in Zagreb.
After a tied first period, Jonathan Weaver gave Pete Russell's side a 2-1 lead, before Craig Peacock made it 3-1 after good work from Ashley Tait.
A third period slapshot from Colin Shields wrapped up the scoring with 11 minutes to go.
Great Britain play Estonia in their second match on Monday.
"I was very happy with that performance," said coach Russell. "We looked good with the puck and really took the game to Croatia, especially in the second and third period."
There were also wins on the opening day of the tournament for Lithuania, who beat Estonia 7-2, and Ukraine, who were 6-1 winners over Romania.
Follow live commentary of GB v Estonia on 5 live sports extra, Monday, 15:30 BST.
Great Britain began their Ice Hockey World Championship campaign with an impressive 4-1 win over hosts Croatia.