Dunstone will play Sweden in the third-place game Sunday. Russia will play Scotland for the gold medal.
“Obviously it sucks right now, for all of us,” said Dunstone. “But I couldn't be more proud of the guys. We've come a long way in the past year and to get third or maybe fourth in the whole world is an amazing thing.
"Hats off to the Russians. They played amazing again. They’re going to kill it in the final tomorrow, but we’ve got to go out and win that bronze now and we’re very proud to be Canadian.”
The Canadian rink of Dunstone, third Colton Lott, second Daniel Grant and lead Brendan MacCuish lost to Scotland in the 1-2 Page playoff game a day earlier. They needed to defeat Russia in order to get the rematch, but Arkhipov came through in the extra end to get the berth in the final.
Arkhipov went on the offensive right away in the 11th end and forced misses from the Canadians as they tried to set up for the steal. Dunstone made a hit and roll behind cover on his last throw, but Arkhipov just skimmed by a guard to make the takeout for the win.
Dunstone took the early lead by making a tricky double to score two in the first end. The teams continued to trade deuces through the next four ends.
Tied 7-7 after eight ends, Dunstone gave up a steal of one in the ninth when his takeout attempt flashed by a Russian counter. Canada scored one in the 10th to force the extra end.
Skip Corryn Brown and her team from Kamloops, B.C., did not qualify for the women's playoffs.
Scotland will play Russia for the gold on Sunday. Japan will meet the Czech Republic for bronze.