Matt Cullen assisted on Clutterbuck's first two goals.
Clutterbuck put the Wild in the lead in the first period then scored twice more in the third, when the Wild had four goals.
"We skated well, played hard and created turnovers," Clutterbuck said. "Maybe our intensity was a bit better.
"After the second period where we flattened out a bit, we regrouped well. We said, 'Let's get after them, get the puck to the net and make the obvious plays."
Defenseman Jyrki Jokipakka of Finnish League team Ilves scored in the second period after Eric Nystrom failed to clear the puck.
Niklas Backstrom had 24 saves.
The Wild will face the Carolina Hurricanes to open the NHL season in Helsinki on Thursday and Friday.