Dowsett was part of a six-man breakaway, also including compatriot Matthew Holmes, that was allowed to go free on the 200-kilometre stage eight from Giovinazzo to Vieste.
And he rode away from his fellow escapees inside the final 20km as he used his time trialling skills to take victory by 75 seconds.
It gave the Israel Start-Up Nation rider his second career Giro stage win, seven years after his success on the stage eight time trial of the 2013 edition, and a first Grand Tour victory for his young team.
Israel Start-Up Nation may be signing Chris Froome next year, but Dowsett's own future is uncertain in the final months of his contract, making this victory all the more significant.
"It's been such a tough year," said Dowsett, who is due to become a father in the coming months.
"Just all the uncertainty and trying to work out how I'm going to get to next year and still be racing, still be doing what I love, and still being able to put food on the table for three of us rather than two come January.
"Hopefully this year will help secure something for next year."
Holmes was beaten to second place by Salvatore Puccio, while the peloton eventually rolled home almost 14 minutes behind, with Deceuninck-QuickStep's Joao Almeida retaining the pink jersey and his 43-second lead of Pello Bilbao of Bahrain-McLaren.
There was no change at the top of the overall classification, with the likes of Vincenzo Nibali, Jakob Fuglsang and Steven Kruijswijk still bunched up closely behind.
Dowsett's victory was a dose of British success hours after Mitchelton-Scott announced that Yates had tested positive for coronavirus after developing "very mild symptoms" following Friday's stage seven.
Yates, who began the race among the overall favourites, was isolated in his hotel room and left the race in an ambulance to begin a period of quarantine, but his positive test leaves questions for the Giro itself after the virus penetrated a team bubble.
Mitchelton-Scott team doctor Matteo Beltemacchi said: "Simon displayed a very mild temperature on Friday evening during our routine temperature checks, which have been completed three times per day during the course of the Giro d'Italia.
"Following the team's Racesafe Covid-19 policy, he was isolated in his room and we immediately requested a rapid test using the services offered by (race organiser) RCS, which has returned positive."
A follow-up test confirmed the result and Dr Beltemacchi added: "Simon's health remains our main concern and, thankfully, his symptoms remain very mild and he is otherwise in good health. We want to thank the RCS for their support in arranging the quick testing and his transport."
Mitchelton-Scott said their other riders had all returned negative tests and would continue to race, but will be subject to additional testing.
Yates is the first rider to test positive in the Giro, which has not adopted the same "two strikes" rule that would have seen teams sent home from the Tour de France last month if more than one person within their camp tested positive.
Yates, the 2018 Vuelta a Espana winner, had entered the Giro as one of the pre-race favourites after his victory in Tirreno-Adriatico last month.
But he struggled on Monday's stage three on Mount Etna, finishing more than four minutes after stage winner Jonathan Caicedo and more than three minutes down on the main group of overall contenders.
The Bury rider sat 21st overall, three minutes and 52 seconds down on Almeida, after Friday's stage seven to Brindisi.
Yates' exit means that both of Britain's overall contenders in the race are out after Ineos Grenadiers' Geraint Thomas suffered a fractured pelvis in a freak accident with a stray drinks bottle in the neutralised zone of stage three, withdrawing from the race a day later.