Spain are aiming to become the first side to win Olympic gold after lifting the Women's World Cup, having defeated England in the final of that tournament last year.
Ballon d'Or winner Bonmati levelled after Aoba Fujino's stunning 13th-minute free-kick opener in Nantes, before the Spain midfielder teed up Mariona Caldentey's winner 16 minutes from time.
That result saw Montserrat Tome's side seize top spot in Group C ahead of Brazil, who edged past Nigeria 1-0 thanks to Gabi Nunes' first-half finish.
Elsewhere in Group A, defending champions Canada put off-field issues to one side by overcoming New Zealand 2-1 thanks to goals from Cloe Lacasse and Evelyne Viens in Saint-Etienne.
Canada's integrity had been questioned ahead of the game in the wake of a spying scandal, with assistant Andy Spence serving as head coach after Bev Priestman volunteered to sit out.
Priestman, two members of her staff and the Canadian Olympic Committee are being investigated by FIFA's disciplinary committee after a drone was spotted flying over New Zealand's training on Monday.
"Obviously the timing was quite terrible," said Canada captain Jessie Fleming of the drone incident after her side battled back following Mackenzie Barry's early opener.
"But I think for us, we've just leaned into each other as a player group and we really just want to focus on being here and playing."
Hosts France seemed on course for a routine victory in the other Group A game after Marie-Antoinette Katoto's first-half double and Kadidiatou Diani's goal against Colombia.
However, Catalina Usme pulled one back from the spot and Manuela Pavi further reduced the deficit nine minutes later, only for Mayra Ramirez's late red card to help France hold out for a 3-2 victory.
Meanwhile, Germany swept aside Australia 3-0 in Group B, inflicting the Matildas' joint-heaviest defeat at the Olympics, along with a loss against the same opponent by the same scoreline, at Sydney 2000.
Efforts from Marina Hegering, Lea Schuller and Jule Brand sealed the victory for the DFB-Frauenteam against the Tokyo 2020 semi-finalists.
The defending Olympic champions had won both their group matches, but were docked six points after being found guilty of using a drone to spy on New Zealand's training session ahead of their opening match of the Games.
It subsequently saw head coach Bev Priestman banned from football-related activities for a year, and despite appealing the decision, saw it rejected.
However, Vanessa Gilles' header proved to be the difference as she rose highest to meet Jessie Fleming's corner kick delivery in the 61st minute.
While Canada only took three points from their group games, they joined both Spain and the United States as the only teams to win all their games at the tournament so far.
Colombia, who started the day's action in second, settled for third spot but advanced to the knockout stages as one of the best third-placed teams and will face Spain.
Canada, meanwhile, will continue their quest for a second Olympic triumph in the Parc des Princes on Saturday where they will face Germany.
In the other Group A fixture, hosts France confirmed their place in the knockout stages of the competition after a hard fought 2-1 triumph over New Zealand.
Marie-Antoinette Katoto scored the opening goal of the game in the 22nd minute, only for Kate Taylor to respond for the visitors two minutes before the interval.
Katoto, who scored a brace against Colombia in their opening group game, notched her second double of the tournament late on to take her tally to five at the Games and secure top spot for the French.
France will next be in action this Saturday in Nantes, where they will face Brazil, who will be without veteran striker Marta following her red card against Spain earlier in the day.
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.
Gabi Portilho's 82nd-minute goal proved decisive in Nantes as Brazil claimed a place in the semi-finals.
Matters could have been vastly different for France had Sakina Karchaoui converted an early penalty, but she fluffed her lines from 12 yards.
Brazil will face Spain in the last four, while the other semi-final will see Germany take on the United States.
Germany drew 0-0 with defending champions Canada after 120 minutes of action in Marseille.
But Ashley Lawrence and Adriana Leon saw their penalties saved by Ann-Katrin Berger, who subsequently stepped up to slot in the crucial spot-kick as Germany secured a 4-2 shootout victory.
Data Debrief: Quarter-final hoodoo continues for France, Germany meet the USA again
France have now been eliminated at the quarter-final stage in seven of the last eight international tournaments in which they have participated.
Meanwhile, the USA and Germany will meet again in the last four of a major tournament for the fifth time, which is two more than any other match-up in the history of the Women's World Cup and the Olympics.
France are competing in the Olympics for the third time after qualifying as hosts, though they failed to win a medal in either of the previous appearances.
Their best-ever finish came at London 2012, when they finished fourth after conceding a stoppage-time goal in a 1-0 defeat to Canada.
Despite never reaching a major tournament final, Les Bleues are among the favourites to win the gold medal in Paris.
And after regularly reaching the knockout stages of tournaments during Renard's time as captain, she is confident now is the right time for her team to finally get the glory.
"Winning the Olympic gold is the dream," she told The Guardian. "Personally, I rank playing for my country very highly.
"So far it's been a lot of ups and downs, but you learn from the defeats. Life isn't only made up of victories – many winners have fallen again and again before being crowned.
"I hope that our efforts over the years will be rewarded this summer.
"I think there's a bit of fear on the part of the teams we face because we're so well-rounded. But when we look back at the matches in which we were knocked out, we weren't missing a lot. It's the little details that send you home.
"We see that we've fallen behind compared to other countries – even though at one point we were ahead. Now would be the right time to strike, and I say that in all modesty – it would be ideal for us."
France will also face Canada and New Zealand in Group A.
