Dunstone and his Winnipeg team currently sit at 6-2, tied for second place with Russia.
Scotland's Kyle Smith leads at 7-1, while Sweden (6-3) and Norway (5-3) are close behind.
"Win (one ore game) and we're in," Dunstone said after the game. "We just have to do our job there and the rest can sort itself out."
Canada took control in the first five ends of the high-scoring affair. Dunstone scored deuces in the first and third ends before laying three in the fifth for a 7-3 lead.
Norwegian skip Eirik Mjoen scored a single in the seventh end, then turned on the offence in the eighth, forcing Dunstone to miss a difficult take-out and stealing two. But Canada came back with a deuce of its own to lead 9-6 after nine and run the Norwegians out of rocks in the 10th.
"It was a sloppy (eighth) end, we know that we can do better than that, but we still had control of the game," Dunstone said. "That was the positive that we took out of that. We just made sure to score or blank the ninth end and then obviously we got the two."
Canada finishes round robin play against China's Zhongbao Zhang (1-7) on Thursday.
Canadian women's skip Corryn Brown was idle Wednesday will finish off the round robin on Thursday with games against Sweden's Sara McManus (3-4) and Norway's Kristine Davanger (1-7). The Kamloops, B.C., rink has been eliminated from playoff contention.
"It'll be a tough road back here, for sure," Brown said after her Tuesday win over the Miranda Solem of the U.S. "But we definitely took advantage of the experience we had here."