Skip John Shuster and his team wore puzzled looks as they realised they had been given women's medals instead of men's after their 10-7 victory on Saturday.
But Shuster brushed off the mix-up as the team celebrated their famous and unexpected victory, which was sealed by a rare five-pointer with two ends to go.
“It's no big deal,” beamed Shuster, who was competing at his fourth Olympics and was part of the USA team that took bronze in Turin in 2006.
“From the first time we stepped onto the ice to the last rock we threw I'll never stop thinking what these guys have done for me,” he added, smiling at his team-mates.
Sweden, whose skip Niklas Edin made a couple of crucial errors, reduced the gap to three points going into the last end but the Swedes finally conceded with one stone left.
Shuster delivered a hammer (last throw) blow that lifted the Americans five points clear 10-5.
“It feels almost unbelievable, but we came out here with great intensity and just had to believe we could do it, and make our shots,” said America's Matt 'Ham' Hamilton.
Carl XVI Gustaf, the Swedish monarch, was amongst the amongst the 3,000 crowd for the final in Gangneung, as was Ivanka Trump, daughter of US president Donald Trump.
The teams were led out for the curling climax by a kilted Korean playing 'Scotland The Brave' on bagpipes, in a nod to the sport's origins in medieval Scotland.
The Swedes were 2-0 up by the second end, but the US team levelled immediately, and went 3-2 up in the fourth end with their yellow stone deemed an infinitesimal amount closer to the tee than Sweden's red.
The irked Swedes make for dangerous foes and they wasted no time bouncing back, skip Edin throwing a perfect hammer to put the Scandinavians back in front at 4-3.
But to enthusiastic support from supporters in stars and stripes, Shuster had his men back in front at 5-4 after a mistake by his opposite number.
Shuster then pulled off his master throw to secure the US a stunning five-pointer to go 10-5 up and earn the US a famous success.