The game was part of the 2010 Compuware NHL Premiere Challenge series.
Marek Zidlicky and Chuck Kobasew also had goals for the Wild, who closed their preseason slate with their first win (1-4-2).
Jyrki Jokipakka scored Ilves' goal.
"We skated well, played hard and created turnovers," Clutterbuck said. "Maybe our intensity was a bit better."
Clutterbuck made it 1-0 at 11:54 of the first when he scored off a Matt Cullen pass. After Jokipakka's goal in the second past hometown hero Niklas Backstrom, the Wild scored four times in the third.
Clutterbuck scored off another Cullen setup at 7:10 to break the tie, and then Zidlicky provided a nice insurance goal at 13:06 of the period. Working a give-and-go with Andrew Brunette, Zidlicky reached back for a pass behind him, kick it up to his stick and fire a wrister past Finnish goalie Sami Aittokallio, a 2010 fourth-round pick of the Colorado Avalanche.
Clutterbuck banged in a loose puck in the crease to complete his hat trick at 16:59, and then Kobasew knocks in a John Madden shot with 2:26 left for the final score.
"After the second period where we flattened out a bit, we regrouped well," said Clutterbuck. "We said, 'Let's get after them, get the puck to the net and make the obvious plays.'"
Next for the Wild is a trip to Helsinki, where they'll open the season with a pair of games against the Carolina Hurricanes on Thursday and Friday.