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."
Serbia entered the fourth quarter of the game with a 13-point lead, but a stunning late comeback from the USA, who have won gold in each of the last four Olympics, instead saw them prevail 95-91.
Curry starred for Team USA, scoring 36 points, the second-highest scoring game by an individual in the team's Olympic history, and his two free throws in the dying seconds ensured Serbia were unable to force any more drama.
And Curry explained how the lure of a fifth consecutive Olympic gold medal spurred them to avoid the shock defeat.
"We talked about it the whole way, all summer," he said. "No matter how it looked, we were going to be challenged at some point.
"Outside of the exhibition series we had a pretty smooth road. Serbia are tough. They're a great team.
"Playing them three times, it's always hard to beat a team that many times, so to come back the way we did was amazing.
"We have no quit, and we know how much this means to win a gold medal with this group and the moment we have in front of us.
"Obviously, I hit the big three, but our defence carried us. Defence wins games in any league, especially in FIBA, so it was pretty special."
Serbia at one point held a 17-point lead in the first half, with NBA MVP Nikola Jokic getting 17 points and 11 assists, though they floundered in the closing stages.
While Curry took most of the headlines, LeBron James made his mark too, tying the game at 84-84 with four minutes remaining.
He got 16 points, 12 rebounds and 10 assists to finish with a triple-double, becoming the first player ever to complete the feat twice at the Olympics.
He echoed Curry's sentiments on Serbia's strength, noting how that helped to get the best out of the USA.
"Give a lot of credit to Serbia," James said. "They gave us everything they had.
"It's a great team. They played exceptionally well. They tested us and we needed that."
The USA will face hosts France in the gold-medal match on Saturday.
Curry, who helped Team USA to an opening 110-84 win over Serbia, echoed a sentiment pushed by his Golden State Warriors coach, Steve Kerr.
Ahead of the Games, the USA endured a stern test against Wednesday's opponents earlier this month, narrowly avoiding a huge upset with a 101-100 victory in London.
South Sudan are making their first appearance at the Olympics, and got their campaign up and running with a 90-79 triumph over Puerto Rico.
Despite South Sudan not having any current NBA players on their roster, they have plenty of experience within their ranks.
The likes of Wenyen Gabriel, JT Thor and Marial Shayok all shone in their pre-tournament meeting with the USA, with Curry acknowledging a tough task lies ahead.
"We have appropriate fear," said Curry. "We know we can't just sleepwalk through any game and feel like you're going to win."
While the USA are still the clear favourites to win the encounter at the Stade Pierre Mauroy, head coach Kerr said their previous encounter will be to their advantage this time around.
"They came within one shot of beating us," Kerr said.
"I'm really glad that we played them so we can feel their speed and their 3-point shooting ability and feel how good they are."
"We'll be much better prepared [Wednesday]. But doesn't guarantee anything."
During their pre-tournament encounter, South Sudan scored 14 3-pointers against the Americans, making 10 more against Puerto Rico last time out.
"The exhibition schedule was great because you got to figure out where we need to get better and also feel the force of teams that are coming trying to beat us," Curry said.
"They're a very high-octane offense, spread the floor, shoot a lot of 3s and have athleticism. So you just got to be mindful of how to guard them. It's totally different than Serbia."
The United States will go in search of a fifth straight men's basketball gold in the French capital, where they open their Group C campaign against Serbia on Sunday.
After that meeting with Nikola Jokic and company, the star-studded USA team featuring Durant, LeBron James, Stephen Curry, Joel Embiid and a host of other NBA stars take on South Sudan and Puerto Rico.
With Steve Kerr having so much talent at his disposal, the roster has been compared to that of the 1992 'Dream Team', who took gold in Barcelona behind the efforts of Michael Jordan, Magic Johnson, Larry Bird, Scottie Pippen and other great names.
However, at a press conference ahead of Team USA's 2024 opener, Curry reminded reporters that the class of 1992 only faced nine other active NBA players.
Durant is expecting a much tougher assignment this year, responding to Curry by saying: "Everybody is a contender. Everyone is here for a reason.
"We're playing against 65 or 64 NBA players in Paris. So you know they're the best in the world."
Asked to identify the main players to watch from other nations, the Phoenix Suns forward said: "Giannis [Antetokounmpo] or Jokic."
While Durant adopted a cautious tone, Golden State Warriors star Curry was more bullish regarding the USA's gold medal hopes.
Quizzed on who he was most excited about facing, Curry simply said: "Whoever's in the gold medal game."
The United States team is taking shape as they prepare to defend their gold medal at the delayed 2021 Olympics.
Reports at the weekend detailed the expectation Durant would join the team after the Nets exited the NBA playoffs.
Durant was on the victorious USA teams in 2012 and 2016 and this year averaged 26.9 points per game in the regular season and 34.3 in the postseason – the 25th-best mark of all time.
The 2014 MVP will not be the only Brooklyn player on the Olympic team, according to The Athletic.
A hamstring injury limited Harden to 36 regular season games for the Nets following his trade from the Houston Rockets, before he played nine times in the playoffs, scoring an underwhelming 20.2 points per game.
Harden went to London in 2012 after his final season as a bench scorer for the Oklahoma City Thunder but not to Brazil four years later having established himself in Houston.
Golden State Warriors great Stephen Curry was involved on neither occasion – although he won the World Cup in 2010 and 2014 – and will not make his Olympic bow this year either, the report added.
Curry almost single-handedly carried the undermanned Warriors to the brink of the playoffs this year, taking the NBA scoring title with 32.0 points per game.
Donovan Mitchell, who struggled with an injury as the Utah Jazz lost to the Los Angeles Clippers, has also declined an invite, ESPN revealed.
Bam Adebayo, the Miami Heat center, will join the 12-man roster, though, aiming to bounce back from a playoff sweep at the hands of the Milwaukee Bucks in which he scored just nine points on four-of-15 shooting in Game 1.
A star-studded USA side have won all their games in Paris so far, but now the pressure is on in the knockout stage.
Brazil are their quarter-final opponents on Tuesday, and while Curry is confident the USA's attack is good enough to beat any team, he knows each player has to be 100% ready for clutch moments.
"That's how we can overwhelm teams," he said.
"It's just everybody has to be ready for your moment whenever it is."
For coach Steve Kerr, meanwhile, it is a case of the USA sticking to an identity and gameplan.
"It's important to focus on keeping that identity now that you're playing the best teams," Kerr said.
"We know what wins a FIBA game.
"We are just completely focused on our defense and then the beauty of our team and the talent, the depth of our talent is that from one game to the next, we've got lots of guys who have the ability to get rolling."
Kerr's team held off a late charge from France to win their fifth straight Olympic gold, with Curry putting on a masterclass from 3-point range in the latter stages.
Curry shot 8-of-13 from 3-point range, sinking four of those efforts after Victor Wembanyama had dragged France within three points with three minutes remaining.
Despite working with Curry for 10 seasons in his role as Golden State Warriors coach, Kerr cannot get enough of watching the four-time NBA champion.
"Steph Curry ended up being the difference. The flurry at the end of the game was just incredible. Watching him never gets old," Kerr told Eurosport after the game.
"I want to give credit to France; they were amazing. It felt like we were going to break that game open but they just kept hanging in there.
"Congrats to France on the silver medal, it’s a great accomplishment.
"Winning a gold medal is a dream for any young athlete, so to be part of it is incredibly special, and I'm just thankful for the opportunity."
Wembanyama finished with a game-high 26 points for France, while Guerschon Yabusele also had 20 points, 15 of them coming in the first half.
France head coach Vincent Collet said: "For sure, it's a disappointment, because we expected that we could do it but, in the end, we have to recognise they were better.
"This is the greatest moment of my career and, to do it in Paris, it is something special. We had a dream to make it happen but it was impossible, USA were too good."
Team USA – who have won gold at the last four editions of the Olympics – looked set to miss out on Saturday's final when Serbia entered the fourth quarter with a 13-point lead.
NBA MVP Nikola Jokic had 17 points and 11 assists for Serbia, who led by as many as 17 points at one stage in the first half.
Bogdan Bogdanovic had 20 points for Serbia while Aleksa Avramovic had 15, but Serbia were unable to hold on and avenge their 110-84 loss to the USA in the group stage.
Golden State Warriors star Curry carried the USA's offense for most of the game, though it was LeBron James' driving layup that tied the contest at 84-84 with under four minutes remaining.
The USA struggled defensively for long periods but finally began to put real pressure on Serbia late in the fourth quarter, and a missed 3-pointer from Ognjen Dobric with Serbia 86-84 up proved decisive.
Curry put the USA ahead with a 3-point jumper on a James assist with two minutes and 24 seconds left, then layups from both players stretched their lead as Serbia wilted.
Twice Serbia drew within two points in the final minute, only for two Curry free throws to seal the USA's victory with eight seconds on the clock.
They will face hosts France – led by NBA Rookie of the Year Victor Wembanyama – in Saturday's gold medal match, after Serbia face Germany for bronze.
James added 12 rebounds and 10 assists to his 16 points to finish with a triple-double, while USA team-mate Joel Embiid brought up 19 points.
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.
