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.
Hayes, who took charge of the USWNT in May, has won six of her seven games at the helm, conceding just twice in that time.
The USA, along with Spain, are the only two sides to win all of their games at the Paris Olympics so far and will have great confidence heading into the knockout stages.
Trinity Rodman's second goal of the tournament two minutes from half-time sent them on their way, as Korbin Albert's 77th-minute strike saw her become the the youngest substitute scorer for the USA at the Olympics since Mallory Swanson against Colombia in 2016.
Alanna Kennedy's late strike would take some of the shine off an otherwise impressive display, but the United States dominated from the first whistle.
Hayes' side accumulated an expected goals (xG) of 2.82 from the 21 shots they had compared to Australia's 0.46, ending the match with 71.7% possession.
The United States will face Japan in the quarter-finals of the tournament, while Australia face a nervous wait to see if they qualify as one of the best third-placed teams.
In the other Group B encounter, Germany confirmed their place in the knockout stages alongside the United States following a comfortable 4-1 win over Zambia.
Lea Schuller opened the scoring in the 10th minute, with Klara Buhl adding the Germans second of the afternoon shortly after the restart.
Zambia captain Barbra Banda threatened to make the encounter a more difficult affair with her fourth goal of the tournament two minutes later.
But Schuller and Elisa Senß would add further gloss to the performance soon after to secure second place in the group.
Germany's triumph sets up a meeting with the runners-up of Group A, which could be either one of Colombia, France, Canada or New Zealand.
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.
