By Steve Keating

QUEBEC CITY (Reuters) - Antti Pihlstrom scored twice and Niklas Backstrom made 36 saves as Finland beat Olympic champions Sweden 4-0 to claim the bronze medal at the ice hockey world championship on Saturday.

In a rematch of the 2006 Olympic gold medal final won by Sweden, the Finns exacted a small measure of revenge on their Nordic neighbors.

"It's always good to beat Sweden," Finland captain Ville Peltonen told reporters. "For the Finnish people, two weeks in front of the television they get a little bit of a reason to celebrate too.

"But I think Niklas Backstrom made the difference today, we battled hard but I don't think we were that much better, they out shot badly."

Sweden out shot Finland 36-13 but could not put a puck past Backstrom.

The Minnesota Wild netminder was particularly sharp in the final period as the desperate Swedes launched an all-out assault outshooting the Finns 13-3.

Pihlstrom scored his first midway through the opening period, batting a high pass past Stefan Liv.

Janne Niskala added a second to and after a scoreless second Pihlstrom and Mikko Koivu added third period tallies to clinch the bronze.

"A medal is always a medal," said Montreal Canadiens captain Saku Koivu. "We had a lot of people watching the game back home, this is big tournament for European countries, playing against the Swedes we don't want to lose for them."

Canada play Russia for the gold medal on Sunday.

(Editing by Trevor Huggins