Atkinson's goals in the first and sixth rounds were the only goals in the shootout for the U.S., which was outshot 44-25 in regulation and overtime, leaning heavily on New Jersey Devils goalie Keith Kinkaid's 40 saves.
Atkinson also assisted on a goal by Detroit Red Wings center Dylan Larkin, who put the U.S. up 4-3 at 3:27 of the third period. St. Louis Blue defenseman Colton Parayko knotted it, 4-4, at 10:48 of the third, forcing a 3-on-3 overtime in which neither team could score despite getting power plays.
Connor McDavid's tripping penalty with 17 seconds left in OT made him ineligible to participate in the shootout, which took away Canada's captain and top shootout option.
After Mathew Barzal's backhand hit the crossbar to start the shootout, Atkinson led off for the U.S. with a beautiful goal. He picked the puck up at center ice, skated in with speed and scored with a quick backhand-forehand deke that fooled goalie Darcy Kuemper.
Jordan Eberle tied it for Canada, 1-1, in the top of the second and neither team scored another one until Atkinson got his second attempt to start the sixth - capitalizing on an IIHF rule that allows teams to use whichever shooter they want after five rounds.
Atkinson's second goal was the inverse of his first, rushing to the net with speed and scoring with a forehand-backhand deke to beat Kuemper into the stick side. Kincaid then stopped Eberle's second attempt to end the game.
"It's a good win for us," Atkinson told the IIHF. "I thought we started slow and showed them maybe too much respect early on. They were able to get some scoring chances, but over time we picked up some speed."
Atkinson's game-deciding shootout goal counted as the game's fifth goal, which means he opened the tournament with a goal, assist and two points.
Two Blue Jackets prospects also played in the other early game, which was held in Copenhagen (Pool A). Each finished without getting on the scoresheet, as defenseman Vladislav Gavrikov helped Russia defeat France, 7-0, in center Alexandre Texier's world-championship debut.
Blue Jackets forward Oliver Bjorkstrand played for Denmark in the second game held in Herning (Pool B), against Germany.