Chmelevski and Norris each scored in a span of 1:46 in the third period to pull the United States into a 2-2 tie.
Chmelevski scored off a loose puck at the left post at 7:01 to make it 2-1, and Norris scored off a pass from Hughes at 8:47 for a 2-2 tie.
Ylonen scored a power-play goal off a slap shot from the top of the left circle to give Finland a 1-0 lead 11:31 into the second period. Latvala made it 2-0 off a shot from the right point 6:00 into the third period.
After finishing third in Group B, Finland defeated Canada (2-1 in overtime), Switzerland (6-1) and the United States. When asked if he thought his country entered the playoffs as underdogs, defenseman Henri Jokiharju (Chicago Blackhawks) laughed.
"Not really," he said. "I just heard we were underdogs. I thought it was funny so say 'Hi' for them right now. This is the best moment so far of my career."
Finland, which finished sixth on the power play (5-of-25, 20 percent), was 1-for-3 with the man-advantage. The U.S. was 0-for-5 on the power play and finished second (7-for-27, 25.93 percent).
"Luukkonen was tremendous, and I don't know how many shots we blocked but everybody was ready to block some shots," Finland defenseman Oskari Laaksonen (Sabres) said. "I think we just worked so hard on the PK and didn't allow a lot of scoring chances."
Said U.S. captain Michael Anderson: "I thought we had some chances on the power play but we didn't bear down and finish them. They had a couple of big blocks. At the end of the day we have to try and bury some of those."
Oliver Wahlstrom (New York Islanders) thought he had given the United States a 1-0 lead when he scored a power-play goal 9:45 into the first period, but the referee immediately waved off the goal and confirmed the call after a video review revealed Chmelevski was in the crease.
Luukkonen, who lost 4-1 to the United States on Dec. 31, finished with a 1.80 goals-against average and .932 save percentage in six games. Primeau (1.61 GAA, .936 save percentage in five games) lost his first match of the tournament.
"We came together three weeks ago and decided we all wanted the same thing," said U.S. forward Ryan Poehling, who was named tournament MVP. "Some things in life don't go your way. I'm proud of the group we had and what we accomplished. At the end of the day we played hard."