After being found guilty of using a drone to film opponents' training at this and past tournaments, the Tokyo champions had six points deducted, while head coach Bev Priestman has been banned from all football-related activity for one year.
The Canadian Soccer Association (CSA) are considering an appeal against the decision, but those controversies were put to one side when the team took to the field.
Starting the day bottom on -3 points, Canada, led by Andy Spence, had to come from behind to beat France after Marie-Antoinette Katoto put Les Bleues ahead just before half-time.
Jessie Fleming equalised from close range in the 58th minute, but Canada fought back, with Gilles getting some help from the woodwork to secure the win.
Meanwhile, Colombia's comfortable 2-0 victory over New Zealand means they now lead Group A after two games thanks to their goal difference.
Elsewhere, in Group C, Spain booked their place in the quarter-finals with a game to spare after a 1-0 win over Nigeria.
Alexia Putellas' long-range strike maintained La Roja's perfect start to the tournament as they bid to become the first team to win Olympic gold after lifting the Women's World Cup.
In the other group game, Japan ruined the party for Marta, who made her 200th appearance for Brazil in a shock 2-1 defeat.
Despite Mina Tanaka's penalty miss in the first half, Japan launched a comeback after Jheniffer's opener, with Saki Kumagai and Momoko Tanikawa both scoring in stoppage time to move second.
The game of the day came in Group B though, as Australia edged out Zambia in an 11-goal thriller.
Barbra Banda's hat-trick gave the minnows a 5-2 lead, but they could not hold onto it as Michelle Heyman made it 6-5 in the 90th minute to snatch a win.
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.
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.
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.
