Curry shot 8-of-13 from 3-point range in a late masterclass as Team USA held off a late charge from France, sinking four of those after Victor Wembanyama had narrowed their lead to just three points.
It was the USA's fifth straight Olympic gold medal, though Curry's first as he shone on his debut at the Paris Games, and he is cherishing the victory.
"I've been blessed," Curry told NBC after the game. "This ranks very high in terms of the excitement and the sense of relief in getting to the finish line.
"I knew if I got to my spot [to make those late jumps] I could knock it down."
Wembanyama finished with a game-high 26 points for France, while Guerschon Yabusele also had 20, with 15 of those coming in the first half.
Despite falling just short in their late comeback, Wembanyama was in high spirits after claiming silver, though he already has his sights on the 2028 Los Angeles Games.
"I never dreamed of this moment," said Wembanyama. "It is incredible. I couldn't have asked for a better team, better coaches.
"The games were really high intensity, and we could have lost by 20 points, but we kept fighting. I will be going for gold in four years' time."
Yabusele, who plays his domestic basketball with Real Madrid in Spain, top scored with 17 points to lead the hosts, who were silver medallists in Tokyo three years ago, to another final.
Isaia Cordinier added 16 points to France's total, while San Antonio Spurs star and NBA Rookie of the Year Victor Wembanyama had 11 points and seven rebounds.
Dennis Schroder led for Germany with 18 points, with Fritz Wagner the only other player to reach double figures against the Olympic hosts.
Germany's loss brought an end to their incredible recent run stretching back to last year's World Cup, having won 12 consecutive games in major international competitions.
France will now face either the United States or Serbia in Saturday's final, with LeBron James and company hoping to win Team USA's 17th gold in men's basketball.
Canada were unbeaten coming into this game after a strong showing in the competition so far, but had no answers against the hosts and their raucous home support.
Canada's game plan limited Victor Wembanyama to a supporting role as he scored just seven points, but that allowed Guerschon Yabusele and Isaia Cordinier to shine as they scored 22 and 20 points respectively.
France made a strong start, storming into a 19-point lead at the start of the second half, though Canada clawed themselves back to within five points with only four minutes remaining - Shai Gilgeous-Alexander led them with 27 points.
The comeback soon stalled though, as Evan Fournier put together seven quick points to send France cruising into the next round as they aim to better their silver medal from the Tokyo Olympics.
They will face Germany for a chance to play in the gold-medal match, while Canada have now failed to make it to the final four at the Olympics since 1984.
Despite a slow start by the hosts, which saw them trailing early in the second quarter, Wembanyama helped to steady their nerves in Lille.
The NBA Rookie of the Year last season came away with 19 points, nine rebounds, four steals and three blocked shots as he inspired his nation in front of a sell-out crowd.
France did not fully seal the victory until late on though, with Nicolas Batum's 3-pointer putting them up by 10 with less than a minute and a half remaining before Wembanyama's dunk made sure of the points in the next possession.
"I knew it was going to be a good day," he said.
"You can't underestimate the power of the crowd, the home crowd. I think it's really going to be the sixth man for this whole tournament."
Meanwhile, team-mate Evan Fournier was quick to heap praise on the 20-year-old after the game.
"I think he did pretty damn good," he said. "He can do so many things that sometimes it's like a burden because he doesn't focus on just one thing."
France will face Japan in their second game of Group B on Tuesday before their final match against Germany.
Steve Kerr's star-studded United States side required a thrilling comeback to beat Nikola Jokic's Serbia in the semi-finals on Thursday, but a far better start put them on course for glory against the hosts in Saturday's gold-medal match.
The USA went into half-time with a nine-point lead thanks to some excellent early work from Devin Booker, though Guerschon Yabusele's 15 first-half points kept France in it, the highlight being a poster dunk on LeBron James.
France shot just 3-of-16 from field range through the first two quarters but got hot in the third quarter, outscoring the USA 25-23 to give themselves hope of a comeback.
Roared on by a vocal crowd at Bercy Arena – where Joel Embiid received plenty of jeers after rejecting the opportunity to represent France – the hosts made up more ground early in the fourth, thanks primarily to the efforts of Victor Wembanyama.
The NBA Rookie of the Year finished with a game-high 26 points – his first 20-point haul at the Paris Games – while also adding seven rebounds, dragging France to within three points with just under three minutes remaining.
However, Curry took charge from there, quietening the crowd with a majestic 3-pointer, his fifth of the game, and adding a further three jumpers before the buzzer.
The Golden State Warriors star finished with 24 points and was 8-of-13 from 3-point range, having also produced an incredible 36-point performance in Thursday's win over Serbia.
A couple of Kevin Durant free throws and a Booker layup helped the USA stetch their lead in the dying stages, claiming a record-extending 17th Olympic gold in men's basketball.
France, meanwhile, had to settle for a third silver in men's basketball, having also been beaten finalists at London 1948 and Sydney 2000.
Japan looked set to cause an unlikely upset against the hosts, but Matthew Strazel's four-point play with 10 seconds of the fourth quarter remaining spared their blushes.
"The shot of his life," Wembanyama said on Strazel's shot that sent the game into overtime at the Pierre Mauroy Stadium in Lille.
Wembanyama then took centre stage, scoring the first eight points of overtime to give France a 92-84 cushion.
Japan would battle back and got to within two points of their opponents, but the home team were able to close out the contest at the free throw line.
Wembanyama also finished with 11 rebounds and six assists, and recalled the moment when the encounter changed in overtime.
"The realisation, the dynamic of the game," Wembanyama said.
"They were playing like underdogs and we were waiting for them to punch a little bit too much. I wanted to make a point and punch first in overtime. And it worked."
France remained in second place in Group B behind fellow unbeaten nation Germany, with the pair squaring off this Friday to see who will finish on top.
Dennis Schroder starred for Germany in the final game on Tuesday, as the Brooklyn Nets point guard notched 20 points and six assists in their 86-73 win over Brazil.
