Swanson strike hands USA Olympic women's football gold against Brazil
Brazil fought hard on a hot afternoon at the Parc des Princes, but the USA struck just before the hour mark when Swanson -– on her 100th cap -- ran through to finish past goalkeeper Lorena.
It is the first time the USA have taken the Olympic title in 12 years, their gold in Paris adding to those won in 1996, 2004, 2008 and 2012.
They have now beaten Brazil in three of those finals, with the South Americans again having to settle for silver just as they did in Athens in 2004 and in Beijing four years later.
It was not quite the ending that their legendary captain Marta was hoping for, as she bowed out of her sixth and last Olympics aged 38 with a third silver medal.
Yet Brazil were never expected to get this far, while the USA's victory confirms their renaissance under new English coach Emma Hayes.
She only arrived from Chelsea in late May but has worked wonders in a short space of time with a team that a year ago was sent packing from the World Cup in the last 16.
"I am very emotional. It has been a dream of mine to be in this position," Hayes told broadcaster Eurosport.
She described her team as "tremendous people and players and role models, I love them."
That World Cup campaign in Australia and New Zealand was the international swansong for USWNT icon Megan Rapinoe, who was among the crowd for Saturday's final, as was Tom Cruise.
Much of the talk in the build-up to the final was about Marta, with the Brazil great free to return for a farewell Olympic appearance after serving a two-game ban for a red card in her team's last group outing.
But the 38-year-old multiple winner of the FIFA world player of the year award was left on the bench at kick-off by coach Arthur Elias.
Perhaps he was mindful of the energy-sapping conditions, and the need for his team to match up physically to the USA.
A younger Marta had played in Brazil's defeats in the 2004 and 2008 finals, both of which came in extra time.
This was also the second clash between the nations in a final this year, after the USA won 1-0 in the CONCACAF Gold Cup in San Diego in March.
The USA subsequently welcomed Hayes as coach and she oversaw wins against Japan and Germany in the knockout rounds to get to the Olympic final.
Marta's farewell
Brazil, meanwhile, scraped through their group as a best third-placed team, before surprise wins against hosts France in the quarter-finals and World Cup holders Spain in the last four, both achieved without Marta.
Their direct approach posed problems to the USA defence in the first half, and they had the ball in the net just over a quarter of an hour into the game.
Ludmila turned Naomi Girma inside out in the box before finishing, but the goal was disallowed for offside.
Swanson was denied at the other end by Lorena after flying down the left wing and bursting into the box, yet it was Brazil who had the best chance of the opening half.
Captain Adriana crossed from the right in stoppage time for Gabi Portilho to divert the ball towards goal, but Alyssa Naeher produced a fine save.
The Americans boasted the more dangerous attack, though, and they went ahead on 57 minutes when Korbin Albert released Swanson to advance and finish expertly for her fourth goal of the tournament.
Brazil sent on Marta for the final half hour, but they never seriously looked like equalising.
The veteran sent a late free-kick over the bar before Naeher kept out Adriana's header in stoppage time as the USA secured a third straight 1-0 win to take the title.