Vanek opened the scoring with a wrist shot that beat Anaheim goaltender Jonas Hiller 4 minutes into the game. He added another goal that made the score 4-1 with 8 minutes to play in the second period.
Miller saved 29-of-30 shots he faced. Anaheim's Nate Guenin, scoring early in the second period, had the lone Ducks goal.
Ville Leino had a first-period goal and Jason Pominville, with an assist from Vanek, scored about a minute after Guenin for a 3-1 Buffalo lead.
Anaheim and Buffalo were among NHL teams selected to open the 2011-12 NHL regular season with games in Europe. In addition to Friday's game in Helsinki, Buffalo will play the Los Angeles Kings in Berlin and the Ducks face off with the New York Rangers in Stockholm, Sweden. Both games are Saturday.