Peters claimed the biggest win of his career alone on the 181km ride from Commezzadura to Anterselva/Antholz with Esteban Chaves (Mitchelton-Scott) second at one minute 34 seconds and Davide Formolo (BORA-hansgrohe).
“I never won a pro race before, not even a Category 1 race, so to win in the WorldTour and at the Giro, it’s enormous," Peters said.
"It’s a relief after so many escapes I've been making for more than a year. I’m not fast enough in the sprints and I’m not one of the best climbers, so breaking away is my only way to win.
"I caught the opportunity with 16km to go. I tried and it worked, it’s fantastic.”
Carapaz (Movistar) now leads Nibali (Bahrain-Merida) by one minute 54 seconds with Roglic (Jumbo-Visma) at two minutes 16 seconds.
Movistar strengthened its position with fourth-placed Mikel Landa closer to the top three on the overall classification at just over three minutes, providing a backup should the team leader Carapaz falter in the defence of his leading position.
“I saw Miguel Angel Lopez (Astana) attacking and I took his wheel to profit from his action," Carapaz said. "We took a small advantage.
"Those seven seconds help me for the closing time trial in Verona. My lead now is significant but, by Sunday, if I can increase it, it would be even more comfortable.
"It would be nice to be two riders from Movistar, Mikel Landa and I, on the final podium.”