Galmarini claimed victory by 0.43 seconds from local favourite Lee, who claimed his country's first ever medal in a snowboard event, as Slovenia's Zan Kosir defeated Sylvain Dufour of France in the small final to complete the podium.
Galmarini finished second to Russia's Vic Wild in Sochi four years ago but the Swiss had enough in the tank this time to overcome a local rider when he defeated Lee in the final.
Lee's semi-final win over Kosir, guaranteeing the hosts a first ever Olympic snowboarding medal, was greeted by huge cheers from the crowd, who had turned up in huge numbers for the last day of action at Phoenix Snow Park.
Kosir matched his bronze medal from Sochi with victory over Dufour, who struggled to maintain the speed that had carried him into the semi-finals.
In PGS, two boarders compete against one another on parallel courses, with the athletes holding the highest seeding from qualification choosing their preferred course; red or blue.
The red course appeared to be the fastest throughout competition and Galmarini said he wanted to go fast right from the start to ensure he had the best chance to win.
"I knew I was in good shape but I just wanted to ride without fear, go hard into every turn and if it doesn't work out then walk away proud and if it does work then even better," said the Swiss, who qualified in first position.
"That was my first thought; just go hard in every run and not think about the consequences.
"There are some races where choosing is important, others not. In this one I wanted to go hard and take risks in qualification to have the result on my side."
Nevin said he was still coming to terms with being an Olympic champion.
"Today was fantastic," he added. "Now I am the Olympic champion. It sounds both surreal and fantastic."
(Reporting by Jack Tarrant; Editing by John O'Brien and Sudipto Ganguly)
