Norway took a 2-0 lead with goals 73 seconds apart from Ken Andre Climb and Anders Bastiansen in the first period.
But Palmieri, who played for the New Jersey Devils, started the comeback and also scored the winner after Jack Skille tied it at 2.
"Norway's a good team," Palmieri said. "They came out strong and we were sitting back little bit at the beginning, but we realized that we had to change the momentum a little bit and during the second period we started to play a lot better."
The American players said their focus remained solely on the tournament.
"Every game for us is emotional," U.S. captain Mark Stuart said. "Playing for our country every game is big and emotional. Nothing's changed for us. Our emotion level is pretty high to start with."
"We're just here to play hockey," forward Derek Stepan added. "We're just trying to have some fun."
Craig Smith finished the scoring with a power-play goal to put away the Norwegians, who stunned Sweden in their first game.
Ryan Shannon added two assists and Al Montoya finished with 13 saves for the United States.
"We didn't come out for the start we wanted to," Stuart said. "But we came back and played pretty well in the second half of the game."
The U.S. outshot Norway 49-15 and will face Sweden in its final Group C match on Wednesday.
Sweden got its first victory by beating Austria 3-0 in Kosice.
Finland needed a late goal from Niko Kapanen to force overtime. In the shootout, Finnish goalie Teemu Lassila saved the first two Latvian attempts while Jarkko Immonen and captain Mikko Koivu both converted.
Niklas Persson scored twice and Magnus Paajarvi added another goal to help Sweden rebound from the loss to Norway.