Vince Trocheck added an empty-net goal for the Americans, who defeated Canada 5-1 in the semifinal.
Filip Sandberg put defending champion Sweden ahead on power play early in the second period, but Grimaldi scored twice in a three-minute span to swing the game in the Americans' favour.
He powered from behind the net for his first, and then redirected Jacob Trouba's slapshot from the blue-line midway through second period.
Sweden pulled its goalie for an extra player with 1:42 left but failed to capitalize. Instead, Trocheck rounded off the win with 16.7 seconds left.
John Gibson made 26 saves for the victory and was named the MVP of the tournament. Niklas Lundstrom had 31 saves for Sweden.
"I couldn't be more proud of our players and staff," said U.S. coach Phil Housley. "And I'm also really happy for hockey fans in our country. This was a total team effort throughout the tournament. It was a very difficult challenge tonight against an excellent Swedish team."
It was the third title for the Americans, who also won gold in 2004 and 2010.
Earlier, Valeri Nichushkin scored in overtime to give Russia a 6-5 victory over Canada in the bronze-medal match.
It was the first time since 1998 that Canada finished without a medal at the event.