Nick Bonino (Vancouver Canucks) and Charlie Coyle (Minnesota Wild) each had a goal and an assist for the U.S. Trevor Lewis (Los Angeles Kings) also scored.
Czech Republic goaltender Ondrej Pavelec (Winnipeg Jets) made 13 saves.
The victory avenges a 4-3 loss to the Czechs in the quarterfinals of the 2014 Worlds. It's the first medal for the U.S. since winning the bronze in 2013.
"It means a lot to USA Hockey," U.S. head coach Todd Richards (Columbus Blue Jackets) said. "Before the tournament, I don't think anyone really gave us a chance to win anything.