The Americans plays Canada at Ufa Arena on Thursday. Defending champion Sweden faces either Russia or Switzerland in the other semifinal game.
Gaudreau scored the lone goal of the first period when the Czechs were two men down at 11:45, and doubled the lead on a power play just 28 seconds into the second period. Ryan Hartman made it 3-0 with a shot from the left circle 40 seconds later, and the Czechs substituted goalie Patrik Bartosak for Matej Machovsky.
Barber scored into an empty net on a power play at 28:44 and beat Machovsky in a one-on-one less than 4 minutes later.
Gaudreau, unmarked at the right, had his third goal on a power play at 39:47. JT Miller capped the scoring with a slap shot from the blue line, capitalizing on a two-man advantage early in the third period.
John Gibson made 31 saves for the victory.
"We played the game we needed to play tonight. You haven't seen our best hockey," U.S. captain Jake McCabe said. "The team that wins the tournament is the team that gets better every game. You have to improve every game. Playing Canada is going to be emotional again. We're going to be ready for it."
Canada edged the United States 2-1 in the preliminary round.
In the relegation round Wednesday, Finland beat Germany 8-0 with Ville Pokka and Aleksander Barkov scoring two goals each.
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