"It was difficult, they have a good team, they work hard and they proved that," Nash said. "It's a great rivalry. ... It was a tough game, but we enjoyed it."
Ty Conklin made 49 saves for the U.S.
"Satisfied? Not really," Johnson said. "It's a loss, no matter how it looked ... it was a loss."
Canada outshot the U.S. 52-20 in the game and 14-4 in the first period, but couldn't immediately find the net.
After a scoreless first period, Mike Komisarek scored what looked like a soft goal from inside the blue line to give the U.S. a 1-0 lead 4:13 into the second.
Reimer said he would probably never concede a goal like that again.
Brent Burns equalized two minutes later, but Blake Wheeler set up the second U.S. goal later in the period, with Jack Johnson scoring on a breakaway.
Canada came back again through John Tavares, who scored 3:27 into the third, and took the lead when Jason Spezza scored on a power play.
Derek Stepan tied the game with 8:43 remaining, forcing overtime with his first goal of the tournament.
"It's a big game for us," Stepan said. "We came up a little short. But I feel we played pretty well, we played the right game."
Canada pressed for a winner, but Conklin stood firm.
"He made some great saves out there when it was 3-2," Nash said. "We could win 4-3 but during the end of the game he made some key saves, he's a good goalie."
Canada coach Ken Hitchcock was pleased with his team's performance.
"We played really well from start to finish," he said. "I was really impressed with the way our players refused to get frustrated and just kept coming and coming."
In Bratislava, Marek Zidlicky, Martin Havlat and Patrik Elias scored to lead defending champion Czech Republic to a 3-2 win over host Slovakia, securing a spot in the quarterfinals. Finland prevailed in a penalty shootout to beat Germany 5-4.
In Kosice, Sweden beat France 4-0 with goals from Robert Nilsson, Oliver Ekman Larsson, Patrik Berglund and Staffan Kronwall
Finland has five points in Group E, while Germany has seven and is closing in on a berth in the quarterfinals.
Patrick Reimer gave the Germans a 4-3 lead with 57 seconds remaining in the second period before Tuomo Ruutu equalized with 5:48 left in the third.
Captain Mikko Koivu scored the winning penalty.