It's Canada's sixth straight gold medal at the summer event, co-hosted by the Czech Republic and Slovakia.
Canada looked dominant in a rematch of last year's under-18 world championship final, which Canada won 3-2.
"When you put the Canadian sweater on, there's a lot of pride," Canada coach Dale Hunter said. "These kids here had a lot of pride at that's what they're going to bring when the (under-18) world championships come next year."
Michael Dal Colle opened the scoring at 3:58 of the first period. Canada took a slashing penalty 30 seconds later, but prevented the United States from capitalizing to get back in the game.
From there Canada kept the pressure on the U.S., while Billia took care of what chances the Americans managed to get.
"You're going to get some shots against, and when they were there he was solid," Hunter said of Billia. "He was really good on rebounds and didn't give them a second shot."
Jayce Hawryluk made it 2-0 with a second-period goal, then Aaron Ekblad and Brendan Lemieux scored in the third to put the game away.
Spencer Watson added three assists to give him a tournament-high 10 points (four goals, six assists).
Hunter had praise for Canada's penalty-killing unit, which kept the U.S. scoreless in three opportunities.
"There weren't a lot of penalties, but they were at key moments of the game," Hunter said. "When you kill them off it gives the rest of the team momentum."
Alex Nedeljkovic made 26 saves but took the loss in goal for the United States.
In the bronze-medal game, Lukas Vopelka scored with 1:25 left in regulation as the Czech Republic beat Russia 3-2.Suggest a correction