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Another four bronzes - in cycling, shooting, judo and gymnastics - lifted Team GB to ninth in the medals table.
Laugher and Mears claimed GB's first Olympic diving title with victory in the men's synchronised 3m springboard.
Clarke won kayak K1 gold, while there were bronzes for Chris Froome, Steven Scott, Sally Conway and Max Whitlock.
Whitlock's medal was Britain's first in the men's all-around gymnastics competition for 108 years and took GB's haul at the 2016 Games to 12.
They now have three gold, three silver and six bronze.
Day five: All the action as it happened in Rio
Day six: What to look out for
Full Rio Olympics medal table
The flurry of success puts GB three ahead of their medal tally at the end of day five in London 2012.
Andrew Willis almost made it seven medals on day five when finishing fourth in the men's 200m breaststroke, won by Kazakhstan's Dmitriy Balandin.
Elsewhere in the pool, Katie Ledecky won her third Rio gold when guiding the United States to victory in the women's 4x200m freestyle relay final.
Michael Phelps stayed on course for a 22nd Olympic title as he beat US team-mate Ryan Lochte in the 200m individual medley semi-final, and 18-year-old Australian Kyle Chalmers won the men's 100m freestyle.
The British diving pair scored a total of 454.32 to end China's hopes of a clean sweep of diving golds at the Games.
It was a particularly emotional victory for Mears; the 23-year-old from Reading had life-saving surgery to remove a spleen ruptured while diving in 2009.
"I still can't really believe that it's happened," said Mears. "I've come from death's door to here. I'm pretty proud."
Laugher, from Harrogate, and Mears both train with the City of Leeds Diving Club. To celebrate their success, Leeds Civic Hall will be lit up by golden lights.
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Clarke, a 23-year-old from Stone in Staffordshire, was inspired as a child by rowing legend Sir Steve Redgrave and began paddling aged 11 on a kayaking trip with the Scouts.
He has a photograph on a wall at home that five-time Olympic gold medallist Redgrave sent him, signed with the words: "Leave no stone unturned."
Clarke was not among the gold medal favourites before the Games but took the title in a time of 88.53 seconds for Britain's first triumph in the men's K1 since Campbell Walsh at Athens 2004.
"I'm gobsmacked," said Clarke. "I knew I was capable of such a performance, but to put it down in the Olympic final is just a dream come true."
16:54: Bronze - Cycling: Chris Froome caps what he calls an "amazing summer" in the men's time trial, just weeks after his third Tour de France win.
19:29: Bronze - Shooting: Steven Scott prevails in a dramatic double trap shoot-off against compatriot Tim Kneale.
19:46: Gold - Canoe slalom: Joe Clarke triumphs after setting a marker which the final two paddlers could not beat.
20:40: Bronze - Judo: Sally Conway loses her -70kg judo semi-final but wins the bronze bout.
21:13: Gold - Diving: Jack Laugher and Chris Mears make history with Britain's first-ever Olympic diving title in the synchronised 3m springboard.
22:40: Bronze - Gymnastics: Max Whitlock secures GB's first medal in the men's all-around event since the London Games of 1908.
Analysis - BBC chief sports writer Tom Fordyce: "After four days that were steady rather than superlative - a brilliant gold for Adam Peaty and three silvers but also six fourth place - this was the day it all turned around for Team GB.
"If not quite Super Saturday, it was certainly Welcome Wednesday, a reminder of one of the most uplifting elements of that magical fortnight at London 2012: the sudden fascination in sports otherwise ignored for four years, the sudden delight in discovering fresh heroes."
Rio 2016 organisers said the green water in the Maria Lenk Aquatics Centre pool will be rectified "soon".
However, they said more should have been done to prevent the problem.
The International Swimming Federation said the pool changed from its usual blue because water tanks had run out of certain chemicals.
But it stressed there had been no risk to the divers.
Security has been increased at the Olympic Equestrian Centre amid reports of a second stray bullet at the venue - this time at the stables.
It is thought the bullets have come from a nearby military compound.
Heavy rain led to the tennis and rowing being postponed until Thursday.
Golf returns to the Olympics for the first time in more than a century, the track cycling begins and there are a total of 19 gold medals to be won.
11:30: Golf - It's missing the world's top four players, who withdrew citing fears about the Zika virus, but the return of golf for the first time since 1904 includes GB major winners Danny Willett (tee off 13:03 BST) and Justin Rose (14:58).
12:30: Rowing - Kath Grainger bids to win a medal at a fifth consecutive Games and become Britain's most-decorated female Olympian. The 40-year-old is in the double sculls with Victoria Thornley.
14:45: Tennis - Resumes after a wash-out on Wednesday. In the men's event, GB's defending champion Andy Murray is second on Centre Court to take on Italy's Fabio Fognini in a last-16 tie. 18:00 British women's number one Johanna Konta faces German Angelique Kerber for a semi-final place.
16:30: Rugby sevens - GB's men face South Africa for a place in the 23:00 final. Fiji and Japan are in the other semi-final.
20:00: Cycling - Action begins inside the velodrome with the men's team sprint qualifying as GB's Jason Kenny, Philip Hindes and Callum Skinner look to reach the final (23:25). Sir Bradley Wiggins begins his quest for a record eighth Olympic medal for GB in the team pursuit (22:23).
03:01: Swimming (Friday): Michael Phelps tries to win a 22nd gold medal in the men's 200m medley. Victory would also make him the first swimmer to win the same Olympic event at four consecutive Games.
Kayaker Joe Clarke and diving duo Jack Laugher and Chris Mears won gold as Great Britain claimed six medals on day five of the Rio Olympics.