Nathan MacKinnon and Sam Bennett also scored, Mitch Marner had two assists, and Binnington made 31 saves for Canada, including six in overtime.
Canada lost 3-1 to the U.S. in the round-robin portion of the tournament at Bell Centre in Montreal on Saturday.
"We lost that game and just to be able to earn this rematch and win in overtime, you can't write it better," Binnington said.
Canada won the gold medal at the 2010 Vancouver Olympics, the 2014 Sochi Olympics and the World Cup of Hockey 2016. It also did so at the 2002 Salt Lake City Olympics and the 2004 World Cup of Hockey, giving it gold in six of the past seven best-on-best international tournaments.
The next best-on-best tournament will be in one year at the 2026 Milano Cortina Olympics.
"For another year at least we have some bragging rights," MacKinnon said. "We've got to go do it again next February."
Brady Tkachuk and Jake Sanderson scored, Auston Matthews had two assists, and Connor Hellebuyck made 24 saves for the United States.
The U.S. still has not won a best-on-best international tournament since the 1996 World Cup of Hockey. That remains its only best-on-best tournament win.
"It just makes us hungrier," U.S. defenseman Zach Werenski said. "We know now that we're neck and neck with Canada. We expect to be in those games with them and expect to win. I think that's exciting for this group. It gives us a lot of confidence that our time is coming, our time is now. It's exciting."
McDavid delivered in overtime from the left hash marks. He got the puck from Marner with no one around him and roofed a shot into the far corner.
He was named the player of the game.
"We just needed one look and Connor was very open, so that was nice," MacKinnon said. "Usually when he's that open it's in the net. We're neck and neck, USA and Canada, but it feels good to be on top this time."
MacKinnon was named the tournament's most valuable player after leading all players with four goals, including the one that gave Canada a 1-0 lead 4:48 into the first period. He scored from the point with a wrist shot through traffic.
The U.S. tied it 1-1 on Tkachuk's goal at 16:52. It was the second shift for Tkachuk, Matthews and Matthew Tkachuk, a line change that Sullivan first went to about three minutes before the goal.