Jennifer Wakefield scored what was the shootout winner when goaltender Shannon Szabados stopped Hilary Knight in the fourth round of extra shots. Meghan Agosta-Marciano also scored and Szabados stopped three of four shots for Canada in the shootout.
"I thought about jumping into the boards, but I didn't want to celebrate too hard in case they went down and scored," Wakefield said. "But a lot of credit to Szabados stopping three of the four. That was phenomenal."
The hosts trailed 2-0 after two periods. Captain Hayley Wickenheiser skated to the bench and headed for the dressing room in the second period. She did not return to the game.
Knight was the first shooter for the U.S. and she scored on that attempt before Szabados foiled her second.
The Americans had the momentum until Canada's Rebecca Johnston and Catherine Ward scored in the final nine minutes of regulation to send the game into overtime.
"We're a confident group and we were able to take it to them in the third," Wakefield said.
Monique Lamoureux and Brianna Decker scored for the U.S. in front of an announced 11,174 at SBP Arena.
Szabados stopped 24 of 26 shots in net in regulation, while U.S. counterpart Jessie Vetter made 27 saves on 29 shots.
Wickenheiser passed the puck up ice during a power play in the second period, skated to the bench and walked to the dressing room.
The 34-year-old suffered a knee injury in the semifinal of the national women's university championship and did not play in the final for her University of Calgary Dinos.
Wickenheiser said at the time the injury was minor and wouldn't prevent her from participating in the world championship.
"Not sure what the injury is yet other than she left the game and was having some difficulty," head coach Dan Church said. "Our doctors haven't reported to me what it is, so she'll be re-evaluted probably now and we'll get a further update in the morning."
In other tournament-openers, the Czech Republic upset Sweden 3-2 in their world championship debut and Russia blanked Germany 4-0 in Group B games. Finland edged Switzerland 2-1 in the other Group A game.
The top two teams in Group A earn byes to Monday's semifinals. The bottom two meet the top two from Group B in the quarter-finals with the winners advancing to the semis. The bottom two teams in Group B play in the relegation round.
Canada wore black and yellow Livestrong jerseys for their first game of the tournament to promote a Nike line of apparel that raises money for the Livestrong Foundation.
The Canadians will be back in red and white Wednesday when they face Switzerland in another Group A game.
The U.S. was quicker to the puck and tighter in their transitions for most of Tuesday's game. Canada didn't convert any of their four power-play chances in the second period into a goal, nor were they able to score on another man advantage in the third.
But drawing the Americans into penalty trouble indicated the Canadians were stepping up their game.
"I think the fact they were taking penalties because we were starting to skate and imposed some of that, that was what we built our momentum off of," Church said. "I believe we need to sharpen up our power play because it wasn't good enough tonight, but I was pleased we were trying to bring the puck to the net more and that caused a few more penalties for them."
Johnston's goal at 11:13 threw a lifeline to the Canadians. They then pressed hard for the equalizer and got it from Ward at 18:13.
Haley Irwin attempted to deflect a Sarah Vaillancourt shot and when Irwin was upended, Ward rushed in to score on the rebound.
Johnston also scored on a rebound during a goal-mouth scramble with Wakefield and Vaillancourt. Johnston put a rebound over the prone American goalie to halve Canada's deficit.
"I would say the attitude in the dressing room was really that we believed could come back," assistant captain Caroline Ouellette said.
"We knew we were better than how we were playing. When you feel that way, you just have to turn it on a little bit more, work harder, talk more and share the puck faster and just keep it simple and put the puck on net. That's what we started to do way more in the third."
The Canadians looked tentative in the face of the American forecheck in the opening period. The U.S. made good on one of two power-play chances in the first 20 minutes and outshot Canada 13-5.
Decker got a second chance on a close-range shot and made it 2-0 at 18:54 of the first period. She shovelled the puck over the outstretched glove and pad of Szabados.
Lamoureux scored a power-play goal on a sharp-angled shot at 4:05. Jocelyne Lamoureux skated the puck out from the boards and fed her twin sister down low.
"Heading into the third period with a two-goal lead, we've got to make sure we're making smart chips, smart pucks," U.S. captain Julie Chu said. "Turnovers are going to cost us and I think that's kind of what happened."
The U.S. handed Canada its worst beating ever to open last year's world tournament with a 9-2 win, although Canada prevailed in the final with a 5-4 overtime victory.
The U.S. named their team Sunday after a five-day selection camp in Lake Placid, N.Y.
Because of the proximity of the CWHL's Clarkson Cup championship and the NCAA's Frozen Four which both included several Canadian players, head coach Dan Church opted not to hold selection camp and instead named his roster March 18.
The Canadian team spent five days training out at CFB Petawawa and played a pair of exhibition games.