Two-time runners-up Brazil were seeking their first gold and thought they had taken the lead early on at the Parc des Princes, only for Ludmila's strike to be rightly ruled out for offside.
Swanson used her pace to break clear soon after but was unable to get the better of Lorena, with neither side truly going close to finding a breakthrough in the first half.
The Selecao suffered a blow early in the second period when Vitoria Yaya was forced off the field on a stretcher and their outing soon got worse when Swanson fired home.
Chicago Red Stars forward Swanson held her line well, latched on to Korbin Albert's throughball and calmly slotted past Lorena with 57 minutes on the clock in Paris.
Brazil could have taken a game of few clear-cut chances to extra-time, but an unmarked Adriana saw her header kept out by Alyssa Naeher in stoppage time as Emma Hayes' team claimed gold.
Data Debrief: Swanson the golden girl for USA
Swanson was denied a dramatic goal on her 99th cap for the USA in their 1-0 extra-time win over Mexico in the semis, but she marked her century in the perfect manner as she scored for the fourth time this tournament.
The 26-year-old is the 44th player in USWNT history to reach that milestone and is the youngest since Amy Rodriguez (25) did so in 2012.
The USA's fifth Olympic gold, coming 12 years after their last success in London, takes them four clear of Germany, Canada and Norway as comfortably the most successful side in the competition.
Brazil secured the gold medal on home soil in Rio five years ago when defeating Germany via a penalty shoot-out, Neymar with the clinching spot-kick for following a 1-1 draw after extra time.
The two nations are together again in Group D, along with Ivory Coast and Saudi Arabia, and are in the same half of the draw as Argentina and Spain, who are both in Group C.
Hosts Japan are joined in Group A by France, Mexico – who claimed the gold medal at the 2012 Olympic Games in London – and South Africa.
Les Bleus will be involved in the opening match when they take on Mexico on July 22 at Tokyo Stadium, followed by Japan taking on South Africa at the same venue later that day.
In the women's event, the United States – winners of the 2019 World Cup - are paired with Sweden, who lost the 2016 final to Germany. Trans-Tasman rivals Australia and New Zealand complete the line-up for Group G.
Japan will take on Canada, Great Britain and Chile in Group E, while the other pool contains China, Brazil, the Netherlands and Zambia.
Men's draw in full:
Group A: Japan, South Africa, Mexico, France.
Group B: New Zealand, South Korea, Honduras, Romania.
Group C: Egypt, Spain, Argentina, Australia.
Group D: Brazil, Germany, Ivory Coast, Saudi Arabia
Women's draw in full:
Group E: Japan, Canada, Great Britain, Chile.
Group F: China, Brazil, Zambia, the Netherlands.
Group G: Sweden, United States, Australia, New Zealand.
USA defeated Brazil 1-0 in Saturday's final at the Parc des Princes through Mallory Swanson's goal just before the hour mark.
Hayes only took over as USWNT head coach in May, after leaving her role at Chelsea, and tasted success in her first tournament in charge.
Speaking to Discovery+ at full-time as the celebrations started, Hayes said: "I'm very emotional. It's been a dream of mine.
"I have to thank my dad - he's the one who pushed me to this position, to be able to come and coach an unbelievable group of players."
Hayes' father, who she has long described as a cornerstone in her football career, passed away last year.
"I've got my dad's necklace on," Hayes said post-match. "It's got an American eagle, and he was with me today and that helped.
"The crowd were tremendous. Brazil were tremendous. I'm just speechless. I'm in shock."
The United States have now won five Olympic golds in the women's final - four more than any other nation - with this their first since 2012.
Swanson calmly converted to give USA the victory in the French capital on her landmark 100th senior appearance for her national side.
This latest triumph comes 10 games into Hayes' tenure and puts the poor showings at the 2020 Games and 2023 World Cup in the past.
"They have received me so well and taken on board everything I've asked," Hayes added. "They're tremendous people, players and role models and I love them."
Brazil have still yet to win an Olympic gold in the tournament, with this their third runners-up finish after also falling just short in 2004 and 2008.
Australia's replies came from Sam Kerr, Caitlin Foord and Emily Gielnik in the seven-goal feast at Ibaraki Kashima Stadium.
It was 36-year-old Rapinoe and 39-year-old Lloyd who stole the show, though, on what may prove to be farewell appearances for the superstar duo.
Whether they play on in the short term for the national team remains to be seen, but this was likely a final outing at the Olympics for both, and they went out in style.
Rapinoe opened the scoring in the eighth minute when her wicked in-swinging corner from the left evaded everybody and found the net.
Kerr levelled seven minutes later with her 48th goal for Australia – a new national team record – when her shot proved too powerful for Adrianna Franch, but it was soon Rapinoe's time again.
The standout player from the 2019 World Cup smashed in her second goal of this game on the volley, connecting sweetly from around 12 yards after Alanna Kennedy sliced an attempted clearance.
Lloyd, who became the outright second most-capped player in US history by making her 312th appearance, got in on the goals just before half time. Her thumping left-footed shot across goal found the right corner, putting the US 3-1 up.
Lloyd scored again in the 51st minute after another Kennedy error, this time a weak header back to her goalkeeper allowing Lloyd a clear run on goal, with the striker slotting home.
That made her the US team's all-time highest scorer in Olympic women's football with 10 goals. Lloyd won Olympic gold in 2008 and 2012, with Rapinoe also on the triumphant latter team in London.
Australia got back into this game with a header from Foord after 54 minutes, and Kerr headed against the left post two minutes later. Substitute Gielnik rattled in a delicious late third for Australia, but they could not find a fourth.
Bird, 40, signed off her Games career in the United States' 90-75 win over Japan on Sunday.
At courtside was Rapinoe, who won a bronze on Thursday when she scored twice as the USA beat Australia 4-3 in the football third-place match.
Rapinoe, who won the Golden Boot and Golden Ball at the 2019 World Cup, first met Bird in the run-up to the 2016 Rio Olympics.
They became a couple later that year and announced their engagement in October 2020.
When the USA clinched the basketball gold medal, Bird went to the side of the court and kissed Rapinoe, later revealing how her 36-year-old partner managed to gain access to the Saitama Super Arena.
"I'm very lucky," Bird said. "Obviously when your partner or your fiancee is also in the Olympics you would love to be able to go and support them, be around them, to give any kind of support possible.
"Megan somehow finagled a media credential and got herself in this arena today. We didn't really know it was going to happen until two days ago, it got confirmed. So I do I feel very lucky she was here to witness it, to share it with me."
Spectators have been blocked from attending venues at the Olympics due to the COVID-19 pandemic, with families of overseas athletes unable to travel to Japan for the Games, meaning Rapinoe was among the fortunate few to be in the arena.
"I just went over and obviously told her I loved her and told her I was tired," said Bird. "That was pretty much the extent of the conversation, and she told me she was happy and proud of me.
"Of course I'm so proud of her and her team for winning that bronze medal. The Olympics is hard. It's really hard. There's so much pressure involved and so to have both of us medal is something that I know we'll take that memory with us forever."
Rapinoe wrote on Instagram: "I am so proud of you @sbird10. As if I could love you any more. Congrats baby!"
Bird has ruled out playing on to Paris 2024, happy to settle for five gold medals, the first of which came in Athens at the 2004 Games.
"It really is hard to wrap your head around it, to grasp what it is," said the Seattle Storm star.
"Twenty years of staying true to the game, making sure you're at the top of your game, so much sacrifice.
"The only thing about getting older, you know all the bad stuff that can happen. We lost in 2006 [to Russia at the World Championship]. We tasted that and that's always been the driver.
"So when we actually have the medal around our necks, it just feels so good. It's a sense of relief in a lot of ways."
USA had 17 attempts on Monday but a second defeat at the Games – they had gone down 3-0 to Sweden in their opening group fixture – means the reigning world champions will not have a chance to secure gold in Japan.
There was controversy surrounding the winning goal, too, as a VAR check resulted in Canada being awarded a penalty for a foul by Tierna Davidson on Deanne Rose in the 74th minute.
Substitute goalkeeper Adrianna Franch, who had replaced the injured Alyssa Naeher in the first half, guessed correctly but Fleming's penalty still found the net.
Canada stubbornly held on for the remainder of the contest to secure a first triumph over their rivals since March 11, 2001.
While USA can still claim a bronze medal, Megan Rapinoe did not hold back when assessing the impact of the result, particularly against opponents they have become accustomed to beating through the years.
"It's a bitter one to swallow. We never want to lose to Canada. I don't think I ever have, so it's a bitter one," Rapinoe said.
"Still a lot to compete for. It's not the colour we wanted, but there's still a medal on the line and that's a huge thing. We want to win that game, but this sucks. It sucks."
Asked why USA had struggled so much to find form during the tournament, Rapinoe replied: "I feel like we haven't had our joy a little bit.
"It just hasn't flowed for us, hasn't been easy. It's not for a lack of effort, or anyone not giving everything they have. It just didn't click for us.
"I don't know if it was roster rotation, I know it's a tough tournament when trying to save people, but our bench is as deep as hell. I don't think we can put it on that, and I can't quite put my finger on it.
"We just didn't have that juice that we normally do."
USA had been aiming to strike Olympic gold for a fifth time having missed out on a medal of any colour at Rio 2016, where they lost to Sweden on penalties in the last eight.
The Swedes lost to Germany in the final five years ago but could still go one better this year – they take on Australia in the second semi-final.
Sweden had sensationally put an end to USA's 44-match unbeaten streak at the start of the women's tournament, with Megan Rapinoe admitting the beaten world champions had "played a bit tight" in a 3-0 defeat.
However, Vlatko Andonovski's side responded impressively to that setback on Saturday, thrashing New Zealand 6-1 in Saitama, in the process registering their largest margin of victory in an Olympics fixture.
Rose Lavelle and Lindsey Horan gave USA a 2-0 half-time lead, the latter on target to mark her 100th cap. Further efforts from Christen Press and Alex Morgan added to the score after the break, while they were helped out by their opponents scoring two own goals.
It is the Swedes who sit on top of the table, though, as a strong second-half performance sealed a 4-2 triumph against Australia.
Meanwhile, Banda equalled the record for most goals scored by a woman at a single Olympics, matching Christine Sinclair's tally of six for Canada at London 2012 with another treble, this time against China.
Zambia's captain scored all her country's goals in a 10-3 loss to the Netherlands in their Group F opener. She followed up with three more in a thrilling 4-4 draw on Saturday, though China's Wang Shuang went one better as she hit four in a see-saw contest.
Vivianne Miedema later moved level with Banda on six goals at this Olympics. The forward had scored four as the Dutch crushed Zambia, then managed another two in a 3-3 draw against Brazil.
Ellen White continued her impressive start to the tournament with the winner as Great Britain defeated hosts Japan 1-0 to qualify for the last eight.
Having scored twice in the opening 2-0 win over Chile, White made it 13 goals in her past 14 international outings when heading in a cross from Lucy Bronze in the 74th minute.
Also in Group E, Canada overcame Chile 2-1 thanks to a brace from Janine Beckie, putting them second in the standings ahead of a clash with Team GB to finish the round-robin stage.
USA - winners of the Olympic tournament four times previously - managed to beat the Netherlands 4-2 on penalties in their quarter-final after the game finished 2-2 at the end of extra time.
Having finished with fewer than six points in the group stage of a major event for the first time in their history, the USA knew a much-improved display was needed against a Dutch side who scored 21 times in their opening three games, the most of any women's side at a single Olympics.
They duly delivered a strong display as they twice took the lead only for Vivianne Miedema to continue her sensational form, scoring twice to cancel out goals from Samantha Mewis and Lynn Williams in an engrossing contest in Yokohama.
Megan Rapinoe swept the decisive penalty kick high into the net after Alyssa Naeher had made two stops to her right.
BRAZIL FALL SHORT AGAIN
Canada await USA after they inflicted further heartbreak on Brazil, whose wait for gold in this event goes on.
Beaten semi-finalists in Rio five years ago, Brazil were held to a 0-0 draw before suffering another defeat on penalties to the 2016 bronze medallists.
Goalkeeper Stephanie Labbe, who was injured in the closing stages of extra time, recovered to make two critical saves in the shoot-out to secure a 4-3 win.
"In the moment, it was about trusting myself, trusting my instincts, and trusting my ability to make a save," she said afterwards.
"Pain is temporary. We have our eyes on the prize."
WHITE TREBLE NOT ENOUGH AS MATILDAS WIN CLASSIC
The stand-out quarter-final took place between Australia and Great Britain, a seven-goal thriller eventually ending in a 4-3 victory for the Matildas.
Two goals from Ellen White had turned the game on its head and looked to be enough to send Hege Riise's side through, but Chelsea star Sam Kerr levelled in the 89th minute with a crisp low strike.
The contest then swung Australia's way in a dramatic minute in extra time, Mary Fowler's deflected shot finding the top corner after Caroline Weir had a penalty saved at the other end.
Kerr scored another before White completed her hat-trick with a deft header to set up a frantic finale, with Australia just holding on for a famous win.
Remarkably, they overperformed in terms of expected goals by 3.2, their highest such figure at these finals.
Australia will contest their semi-final against Sweden, who ended Japan's quest for a medal on home soil with a 3-1 victory.
Mina Tanaka cancelled out Magdalena Eriksson's sixth-minute opener, but Sweden took control in the second half through further goals from Stina Blackstenius and Kosovare Asllani.
USA bounced back from a shock 3-0 loss to Sweden in their opening game with a 6-1 win against New Zealand, but they dropped further points in the round-robin stage on Tuesday.
Previously unbeaten in 44 games before that Sweden loss, USA failed to break down Australia's defence – Alex Morgan's disallowed goal for offside the closest they came to doing so.
Mary Fowler hit the crossbar for Australia and in the end a point apiece was a fair outcome, with the Matildas also advancing to play Great Britain in the last eight.
It is the first time in history record four-time winners USWNT have finished with fewer than six points in the group stage of a major global tournament.
RAMPANT DUTCH AWAIT USA
Sweden were already assured of a place in the last eight ahead of their clash with New Zealand and saw the job through with a 2-0 win at Miyagi Stadium to finish ahead of USA.
Anna Anvegard and Madelen Janogy were on target for Sweden before half-time and they saw out a straightforward win that condemned New Zealand to a group-stage exit.
It means USA will now take on the Netherlands in the next round in what is a repeat of the 2019 Women's World Cup final. The Netherlands lost that match, but they enter this latest showdown in superb form after thrashing China 8-2 in Yokohama.
Lineth Beerensteyn, Lieke Martens and Vivianne Miedema all scored twice in the one-sided affair, while Shanice van de Sanden and Victoria Pelova were also on target.
The Netherlands' tally of 21 goals from three games is already the most scored by a team in a single women's football Olympics event, surpassing the USA's 16 from London 2012.
HOSTS JAPAN SCRAPE THROUGH
Japan did all that they could in the final round of group games by beating Chile 1-0 through a Mina Tanaka goal 13 minutes from time.
That win took the tournament hosts to four points from three games, enough to send them through as one of the best third-placed sides, along with Australia.
Already through to the quarter-finals, Great Britain snatched top spot with a late 1-1 draw against second-placed Canada in Tuesday's other Group E match.
Caroline Weir's long-range free-kick with 84 minutes played took a heavy deflection and cancelled out Adriana Leon's opener.
Brazil also booked their spot in the knockout stages thanks to Andressa's first-half free-kick in their 1-0 win against the tournament's lowest-ranked side in Zambia, who lost Lushomo Mweemba to an early red card.
The Selecao meet Canada in the quarters, while Australia await Great Britain.
Mallory Swanson was denied a winner in normal time, and though Germany pushed for a late equaliser, Emma Hayes will take charge of a final in her first tournament as the USA's head coach.
Unlike in the group-stage meeting between these sides, which finished 4-1 to the dominant Stars and Stripes, it was Germany who almost took a first-half lead, with Alyssa Naeher reacting quickly to get down and push Jule Brand's low shot wide.
In the 86th minute, Mallory Swanson thought she had snatched a late winner – she latched onto Trinity Rodman's throughball and drilled her low shot across goal into the bottom corner, but the offside flag denied her.
Swanson turned provider five minutes into extra time, as Smith timed her run to perfection, darting in behind to beat Berger for power with a wonderful effort.
There was late drama though, as Naeher brilliantly smothered Laura Freigang's close-range header before Smith was denied a second goal at the other end by Berger's quick thinking.
Data Debrief: Smith's touch of gold
Smith has been in top form during the Olympics and netted her third goal in the competition as she carried her team into their 11th major tournament final.
She is also the second USA player to score in at least three consecutive appearances against Germany, after Abby Wambach - five straight from 2009-12.
Meanwhile, it was familiar heartache for Germany as they were eliminated in the knockout rounds of a major tournament (Olympics and World Cup) for the 10th time, with half of those coming at the USA's hands.
There had been pressure on the USA going into the game after two poor warm-up displays, including a 0-0 draw to Costa Rica, but Emma Hayes' team ran out comfortable winners in the former Chelsea boss' first competitive match in charge.
All of the damage was done in the first half, with the Americans three goals up after just 25 minutes in Nice - Trinity Rodman opening the scoring before a quickfire double from Mallory Swanson.
The four-time Olympic gold medallist started as they meant to go on, hitting the crossbar early on through Rodman and Swanson before the former opened her account for the tournament with a drilled finish past Zambia goalkeeper Ng'ambo Musole.
They doubled their advantage thanks to Chicago Red Stars forward Swanson, and she was on hand again to virtually end the contest just a minute later after good work down the left from Sophia Smith.
Zambia's woes were compounded by a red card dished out to Pauline Zulu, which was initially given as a yellow but was upgraded following a VAR review.
Zulu was adjudged to have been the last player when she brought down 18-year-old Smith, and her dismissal all but ended Zambia's slender comeback hopes.
Data Debrief: History made in Hayes' competitive debut
Though the USA had gone into the contest lacking rhythm and form, which raised hopes of a Zambian upset, it was not to be found, with Hayes' side enjoying complete domination from the start. The USA created chances worth an xG of 4.96 to Zambia's meagre 0.37, while they also had 27 shots to Zambia's eight, with 25 of those coming from inside the box.
Hayes became the first coach to win their first major tournament match in charge of the USA by a margin of three or more goals. Meanwhile, with assists in the 17th and 24th minute, Horan is the first player in USWMT history to record two assists in the opening 30 minutes of a major tournament.
Swanson's goals came 66 seconds apart, making them the fastest two goals by a single player in a major tournament in the team's history.
Sophia Smith netted a first-half double on either side of Mallory Swanson's goal before Lynn Williams wrapped up the points late on.
Giulia Gwinn had given Germany hope by equalising, but the USA were too strong as they ruthlessly booked a place in the knockout rounds.
The USA made a quick start, with Smith darting in front of her marker to slot a close-range tap-in past Ann-Katrin Berger, only for Gwinn to cancel it out 11 minutes later with a pinpoint shot into the bottom-left corner.
Emma Hayes' side soon asserted their dominance though – Swanson reacted quickest to latch onto Smith's saved shot, firing in from an acute angle on the left.
Smith then got her second just before the break, helped by a huge deflection, as her effort looped over Berger before bouncing over the line off the inside of the far post.
Jule Brand struck the woodwork just after the hour mark before further misery was piled on the Germans as captain Alexandra Popp was forced off late in the second half with a knee injury that they will be hoping is not too serious.
Williams rounded things off by making a quick impact off the bench, finishing off a lightning-quick counter-attack just under four minutes after coming on.
Data Debrief: Smith and Swanson on song
The USA got the job done in the first half, ensuring Hayes became just the second coach to win each of their first two major tournament matches in charge, after Anson Dorrance in the 1991 World Cup.
Swanson added to her double against Zambia with another goal in Marseille and is just the second player in USA's history to net three times in the group stage of a single Olympics, after Abby Wambach in 2012.
Before today, the winner of each of the five previous major tournament meetings between the USA and Germany has gone on to win the entire tournament, and Hayes will be hoping that is a good sign of what is to come.
The two sides laboured in the first half, with Emma Hayes' team enjoying plenty of possession but struggling to create any meaningful chances at the Parc des Princes.
The USA improved after the break and their first decent opportunity arrived in the 63rd minute when Mallory Swanson exchanged a one-two before curling an effort just wide.
Rodman's influence grew as the game wore on, but it was Sophia Smith who had the best chance prior to the USA's winner, only for the 23-year-old to take too many touches when through on goal, allowing Ayaka Yamashita to close down the angle.
But as penalties approached, Rodman stepped up in the second minute of stoppage time at the end of the first half of the additional 30 minutes, collecting Crystal Dunn’s pass before cutting inside and curling in an unstoppable shot.
Japan substitute Riko Ueki almost equalised from close range, but the USA were able to clear their lines and hold firm to tee up a semi-final against either Canada or Germany.
Data debrief: USA fail to convert possession into opportunities
Despite neither side creating much in the way of chances with the USA mustering an expected goals (xG) of 0.68 to Japan's 0.53, the Americans dominated the ball for large swathes of the match.
They had 71.3% possession, had more than double the passes and final third entries of Japan with 1,026 to 403 and 89 to 44 respectively.
But it ultimately took a moment of brilliance from Rodman to settle the contest. At 22 years and 75 days old, she is the youngest player to score an extra-time goal for the USWNT since Heather O'Reilly at the 2004 Olympics in Athens.
The United States face Brazil in Saturday's showpiece match at the Parc des Princes in a repeat of the 2004 and 2008 finals, fixtures the US won on both occasions.
Hayes, who was appointed as Vlatko Andonovski's successor in May, has won eight of her nine games in charge (D1), scoring 19 goals and conceding just twice.
The former Chelsea head coach won her seventh WSL title in her final season with the Blues, saying her rapid transition to the international stage has been a "whirlwind".
"Going from my beloved Chelsea to the US women’s national team - what a whirlwind and what a dream all at once," Hayes said.
"To finish my time with Chelsea with another Women's Super League title and then be here competing for gold, honestly this is the stuff dreams are made of.
"I have visualised this moment so many times in my life."
Brazil are seeking their first gold in women's football at the Games, and are boosted by the return of Marta, who will play her final international match on Saturday.
The 38-year-old was shown a red card in Brazil's final group game against Spain for a high foot, resulting in her missing the quarter and semi-finals.
Marta has scored 121 goals in 203 appearances for her nation, becoming the first player to score in five straight Olympics with her brace against Japan.
“When I was a young coach assisting Vic Akers at Arsenal, we played a Women’s Cup two-legged final against Umea, the Swedish champions, and they had a young Marta,” Hayes recalled.
“I remember being on the touchline thinking, ‘Oh my goodness, who is this extraordinary player?’ To witness what she’s done on the pitch, I think she’s been more than a role model and icon, she’s been the best player.
“What she’s done for Brazil or the generation coming through, she’s been an inspiration.”
Team USA have the chance to win a first gold medal since London 2012 after winning bronze in Tokyo three years ago.
Despite winning 16 major titles during her time at Chelsea, Hayes is hungry to add to her trophy cabinet while continuing her unbeaten start in the US dugout.
"I like winning, it's part of my DNA," Hayes said. "I'm with a team that likes winning so of course our goal is to win the gold medal."
The 23-year-old's 95th-minute strike proved the decisive goal of the USWNT’s 1-0 semi-final victory against an injury-stricken Germany.
The result means new coach Emma Hayes will have the chance to go for gold in her first major tournament at the helm.
Smith dedicated her goal to the effort of the whole US squad under the ex-Chelsea boss.
"I just saw an open net in front of me and knew I had to step up in the big moment," Smith told NBC. "I felt I had to do that for this team, we've been working so hard.”
