Bobrovsky made 45 stops, some of them spectacular, but couldn’t wrangle the puck when Getzlaf slipped it between his pads during the 3-on-3 extra session.
Carey Price had 24 saves for Canada, which finished 2-1 in exhibitions before the eight-team tournament begins in Toronto this weekend.
The Canadians open the tournament Saturday against the Czech Republic, while Russia begins on Sunday against Sweden.
Canada is a heavy favourite to continue its run atop international play, a surge that started with a triumph at the 2010 Olympics and continued two years ago in Sochi when they grabbed gold again while the host Russians missed the medal stand completely.
Anything less than hearing “O Canada” play after the finals at the end of the month would be a disappointment, particularly on home ice. It’s a role Crosby and his countrymen thrive in though they’ve been a bit uneven during their three exhibitions, following up a 5-2 romp over the US last weekend with an up-and-down performance against Russia.
Crosby and Malkin both joked about facing off against each other on the same sheet of ice they’ve shared as teammates for a decade, with Crosby good naturally saying he may take a friendly shot at Malkin if the moment called for it. The moment ended up coming in the first period, when the two briefly met in the corner before Malkin skated away with both players unharmed.
Canada dominated the first period and took the lead when Crosby fed a streaking Bergeron, who slipped it by Bobrovsky to put the Canadians in front during a 20-minute stretch in which they out shot the Russians 14-5 and tilted the ice heavily to once side.
Russia slowly found its footing and finally converted when Malkin won a faceoff and dropped it to Panarin, who slipped it across the ice to Ovechkin. The Washington Capitals star drilled a one-time from his familiar spot in the left circle to tie it 3:40 into the third. Panarin put Russia up less than four minutes later when he jumped on a rebound to give the Russians the lead.
Tavares picked up his third goal in as many exhibitions by threading a wrist shot from the top of zone by Bobrovsky at 13:58. Bobrovsky sent the game to overtime with a series of spectacular stop in the final minutes of regulation, including a slick glove hand save against Crosby from in close.