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The pair's 10m synchro success and Ed Ling's bronze in the trap shooting took Britain's tally to four and put them 10th in the medal table.
Britain's men missed out on a team gymnastics bronze, while the women's rugby sevens team also came fourth.
Hosts Brazil celebrated their first gold with Rafaela Silva's judo win.
Fortune was not shining for Team GB in the eventing, with William Fox-Pitt slipping out of medal contention going into the final showjumping round.
In the rowing, Britain's Heather Glover and Heather Stanning nearly had their six-year unbeaten run broken by Denmark but a strong finish saw them through to the semi-finals as heat winners.
There was a shock defeat for Irish boxer Paddy Barnes, with the double Olympic medallist losing his light-flyweight bout against Spain's Samuel Carmona.
It was a case of so near yet so far for the men's gymnasts and women's rugby sevens team.
A mistake by Louis Smith on the pommel horse dashed hopes of Great Britain winning a medal in the gymnastics men's team final. They were fourth going into the final rotation, the pommel horse.
Smith, 27, who won individual silver on the pommel and team bronze at London 2012, came off the apparatus during his routine.
Japan won gold, Russia took silver and defending champions China finished with bronze.
Great Britain also missed out on winning the first ever Olympic medal in rugby sevens competition.
Losing two players from the pitch because of yellow cards cost the team in the semi-final against New Zealand. Canada then swept the British team aside 33-10 in the bronze medal match.
There were smiles over in the Olympic table tennis competition where Paul Drinkhall from Middlesbrough became only the third Briton to reach the last 16 of the event with victory over Croatia's Andrej Gacina.
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Norwich-born Nick Dempsey, 35, leads the men's Olympic RS:X windsurfing in Rio after three races at Marina de Gloria.
The 2012 silver medallist won the first two of Monday's three races, before finishing second in the third. He has a five-point lead over defending Dutchman Dorian van Rijsselberghe in the 12-race opening series.
Nick Thompson, in the men's Laser, women's RS:X windsurfer Bryony Shaw are also in contention for medals in their respective events.
In the rowing, red-hot favourites Glover and Stanning reached the semi-finals of the women's pair and the men's four, who have won gold in the event at the last four Games, easily won their heat.
The men's and women's eights and the men's quadruple sculls team reached their respective finals.
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The party does not start until the hosts get a gold - and on Monday Rafaela Silva dominated the country's news bulletins by getting Brazil off the mark.
Silva, 24, jumped over the barriers to be embraced by colleagues, friends and fans after she beat Sumiya Dorjsuren of Mongolia in the 57kg judo.
BBC Americas editor, Leonardo Rocha said: "Silva grew up in one of Rio's most notorious favelas, Cidade de Deus - or City of God - not far from the Olympic venue where she won her gold medal. Her family enrolled her in free judo classes when she was a child to keep her away from gang life."
Silva said: "They said I was a disgrace. Here I am an Olympic champion in my hometown."
There were also plenty of tears at the Deodoro Stadium as Australia won the first Olympic rugby sevens title with a 24-17 win over their Antipodean arch-rivals New Zealand.
Australia's coach Tim Walsh said remarks made by New Zealand counterpart Sean Horan before the match had motivated his team. Horan said Australia did not like to be pressured, nor did they like the physical side of the game.
"But just because they're touch players and they wear ribbons and pig-tails and sing songs does not mean they're not world class rugby players and ruthless in defence and they proved that to everybody," Walsh said.
Only a day after Dutch rider Annemiek van Vleuten suffered a horrific crash in the women's road race, a track cyclist was taken to hospital after an accident in training.
Australia's Melissa Hoskins was taking part in team pursuit practice when the crash happened involving three of her team-mates.
Ashlee Ankudinoff, Georgia Baker, Amy Cure came off their bikes, as did Hoskins who was carried off the track on a stretcher and then taken to hospital as a precaution.
The team pursuit competition begins with qualifying on Thursday.
How do you solve a problem like empty seats at Olympic venues?
Almost 80% of available tickets have been sold, but the TV cameras have focused on barren sparsely populated areas at the arenas.
Organisers have put up billboards of Jamaican sprinting superstar Usain Bolt urging Brazilians to buy tickets inside some arenas.
Rio 2016 chiefs say they are cracking down on tickets touts with around 40 detained inside the Olympic Park on Monday.
Investigations finally got to the bottom of how a stray bullet found its way through the roof and into the media work room at the equestrian venue on day one.
Mario Andrada, the chief spokesman for Rio 2016's organising committee, said a shot had been fired at a police blimp from one of the Brazilian city's favelas.
He said that the intended target was a security camera on the blimp.
Meanwhile, Namibian boxer Jonas Junius was arrested by Brazilian police on suspicion of attempting to sexually assault a maid at the Olympic village.
The 22-year-old is competing in the light-welterweight division.
Over at the tennis competition, play had to be briefly stopped when a man in an Argentina shirt started fighting another spectator during Argentine Juan Martin del Potro's victory over Portugal's Joao Sousa at Olympic Park.
"The crowd always makes a special atmosphere," said Del Potro, who beat world number one Novak Djokovic on Sunday.
"It was beautiful apart from the incident in the beginning. I hope that will not happen again because people need to enjoy the matches and we need to have peace between Argentina and Brazil. This is not football. After that there was a lot of respect so we could enjoy."
It is another jam-packed day of action with 15 golds on offer.
British medal interest will be largely focused on the water and on the gym floor:
14:00 & 18:00 BST Eventing finals: Will Fox-Pitt and his team-mates produce the showjumping rounds of their lives as the team and individual eventing medals are decided?
17:30 BST Canoe slalom C1: Two-time silver medallist David Florence of Scotland will looking to finally looking to win gold as he takes to the waters at the Whitewater Stadium.
16:00 BST Men's rugby sevens: Great Britain's men will be hoping to at least emulate the women as they begin their campaign against Kenya.
20:00 BST Women's synchro 10m platform final: Tonia Couch, 27, and her 16-year-old partner Lois Toulson only teamed up last December but the British pair will be medal contenders at the Maria Lenk Aquatics Centre.
20:00 BST Women's team gymnastics final: Get the Stars and Stripes ribbon ready because Team USA will surely be tying gold around their necks. Great Britain finished fourth in qualifying and have a great chance of a medal.
02:00 BST Swimming finals: Siobhan-Marie O'Connor has come a long way since she made her Olympic debut at the age of 16 at London 2012. She was ranked second in the world going into the 200m individual medley event, and romped through the rounds.
Tom Daley and Dan Goodfellow produced a great final dive to win one of two Olympic bronze medals for Great Britain on day three in Rio.