GB claimed six medals on Tuesday, including two silvers and three bronzes, to take their tally to 13 overall and put them fifth in the medal table.
It more than doubles Britain's previous best medal haul of six after the first four days, achieved at the 2000, 2008 and 2016 Games.
Dean, 21, who contracted Covid for the second time six months ago, edged out compatriot Duncan Scott into second by 0.04secs in the 200m freestyle swimming.
And Georgia Taylor-Brown fought back from a puncture on the last lap of the bike leg to take triathlon silver.
There was also a first medal in 93 years for GB's women's gymnastics team, who took bronze, as did Bianca Walkden in the taekwondo +67kg, matching her result at Rio 2016.
And Charlotte Dujardin pulled level with rower Dame Katherine Grainger and tennis player Kathleen McKane Godfree as Britain's most decorated female Olympian, claiming her fifth career medal as Britain's dressage team won bronze.
She can become the first British woman to win gold at three consecutive Games should she retain her individual title on Wednesday.
Elsewhere, four-time Olympic gold medallist Simone Biles said she had to "focus on my mental health" after pulling out of the women's gymnastics team final.
The American left the arena after the vault, but later returned to support her team-mates as they claimed silver behind the Russian Olympic Committee.
Simon Gleave, head of sports analysis at Nielsen Gracenote, said: "After four days, the expectation was that Great Britain would have 10 medals - three gold, five silver and two bronze medals.
"The forecast for Great Britain has therefore improved to 55 medals including 15 golds. This is likely to be enough for fifth place on the medal table on both total medals and gold medals."
UK Sport set a medal target of between 45 and 70. Team GB won 65 medals at London 2012, followed by 67 medals in Rio in 2016 - finishing second in the medal table.
'Olympic gold seemed a million miles off'
Dean's preparations for Tokyo were badly disrupted by Covid, as he lost more than six weeks of training after contracting the illness twice, leaving him struggling to walk up the stairs.
"When I was sitting in my flat in isolation, an Olympic gold seemed a million miles off," he said.
"I had Covid in September and the new year. The first time wasn't too bad. The second time I wasn't able to train and it was a slow build back into training."
About 70 of Dean's friends and family gathered in his mum's garden in Maidenhead to watch the race in the early hours, with a video of their celebrations going viral.
His mum Jacquie Hughes told BBC One: "We decided, because we couldn't be there, how nice would it be for Tom to know his family and friends were together watching him.
"We invited some members of the swimming club, some neighbours, and before we knew it there were 70 people in the garden watching on a big screen.
"It was so joyous and full of passion. It was lovely. I spoke to Tom this morning and he said he watched the video over and over again."
Dean's team-mate Scott was favourite going into the final after qualifying fastest, but was beaten to the touch in a tight finish.
The result is Britain's first swimming one-two in 113 years, with both men cheered on by Adam Peaty, who retained his 100m breaststroke title on Monday.
Taylor-Brown battles rain, wind and wheel rims to take silver
Taylor-Brown was 22 seconds off the four-strong leading pack going into the run of the triathlon, but reeled in all her rivals except for Bermuda's Flora Duffy to claim an emotional second place.
It is Britain's second triathlon silver after Alex Yee's success on Monday.
The 27-year-old revealed after the finish she had overcome a stress fracture to her leg to make the start line, passing a late fitness test a week before departing for Tokyo.
"My training had gone so well before then though, so that was a bit of a shock, but I knew I had all of that training in the bag," she said.
"I wanted to keep it private. You don't want to show your competitors your weaknesses."
Photo Getty Images Caption: GB swimmer and gold medallist Tom Dean