The 24-year-old Girmay described himself as the "first Black African to win at the Tour", and dedicated the win to the whole continent.
Carapaz became the first Ecuadorian to wear the leader's yellow jersey, taking it from Slovenian Tadej Pogacar who was held up in a late crash on the run to the line.
"It means a lot personally for me and for the continent of Africa," Girmay said.
Girmay is the third African to win on the Grande Boucle after South Africans Daryl Impey and Rob Hunter.
Multiple tour winner Chris Froome was born in Kenya but competed for Britain.
"There are many obstacles for African riders," said Intermarche rider Girmay.
"I had to come to Europe, learn English, learn the cycling language, it takes time and support.
"I should thank my team because with them I have grown every season."
Carapaz and Pogacar are level on time at the top of the overall standings.
Belgian Remco Evenepoel and Danish two-time defending champion Jonas Vingegaard are third and fourth respectively also on the same time.
"I can't remember much about it," said an emotional Girmay at the line.
"I just closed my eyes and hoped for the best at the end."
Girmay pipped Colombian Fernando Gaviria and Belgian Arnaud De Lie after a chaotic finale marked by a late fall as the riders hit speeds of around 65kph in the dash to the line.
The crash, in which the big favourite for the sprint Belgian Jasper Philipsen was involved, created a break in the peloton.
Two-time race winner Pogacar, gunning for a historic Giro-Tour double, did not fall but was delayed.
'A legend now'
Veteran Mark Cavendish was held up by a wheel change as he bids for a record 35th stage win.
The 39-year-old prickly sprinter appeared genuinely pleased for Girmay.
"That's massive, for him, for the Tour, for Africa. He's a legend now isn't he," said Cavendish.
Carapaz came third on the Tour in 2021 but was overlooked in the build up to this Tour after falling on day one last time out.
The Olympic road race champion was also not selected by the Ecuadorian team to defend his title at the Paris Games.
Now the 31-year-old Carapaz has gatecrashed the Fab Four favourites with Primoz Roglic dropping off the pace.
"I was sick after the Tour of Switzerland and I know you need to be in optimal shape here," said former Giro d'Italia winner Carapaz.
"For the first time yesterday I felt much better. Whatever comes after this is a victory, but we will defend the jersey with everything as long as we can."
After two sweltering stages, the skies were shrouded grey entering the northern Italian industrial city with thunder and torrential rain shortly after the race ended.
Girmay is a strong sprinter and modelled his style on Peter Sagan.
He was aided in his win at Turin by the absence of stage favourite Philipsen, who fell in the run in.
The stage winner spoke about his childhood in Eritrea, where cycling is a major sport.
"After lunch in July my dad always used to say 'come on guys, let's watch the Tour de France'.
"One day, after Sagan won and I asked my dad if he thought I could win one day and he said if I worked hard I could.
"But I was inspired too by Daniel Teklehaimanot when he got the polka dot jersey in 2015," he recalled of his compatriot.
"But this is for everyone, they all inspired me, all the Eritrean cyclists."
Girmay signalled his coming of age in 2022 when he became the first African to win a one-day classic at Gent-Wevelgem, aged 21.
It was his second Grand Tour stage win after the Giro d'Italia in 2022 where he injured an eye opening a bottle of prosecco on the podium.
