Russia trailed 2-1 going into the third period, but Sergei Fedorov scored at 4:57 to tie the game.
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With overtime looming, Alexander Semin fed Ovechkin on a break for a shot that goalie Henrik Lundqvist got a piece of, but the puck jumped into the air and landed behind him in the net.
Mattias Weinhandl and Tony Martensson scored for Sweden, while Semin got one in the second period for Russia.
Earlier, the Czech Republic beat Belarus 3-2 in a shootout to stay atop its group.
Radim Vrbata and Ales Kotalik scored in the shootout to help the Czech Republic survive a scare from Belarus.
Belarus was eliminated from the medal round, but earned an important point. With a win over Denmark on Monday, Belarus has a shot at 9th place in the tournament and an automatic berth in the 2010 Winter Olympics.
Belarus goalie Vitali Koval, who made 52 saves against Russia, had 41 against the Czechs.












