Vergne, starting the South American country's inaugural race on pole position, led a Techeetah one-two with German team mate Andre Lotterer.
Swiss racer Sebastien Buemi finished third for Renault e.dams.
Lotterer's and Vergne's cars made contact with four of the 37 laps to go as the German pushed to seize the lead, fortunately without consequences for either.
"It's racing in the end and I had a lot of pace in the car. He knows exactly how to defend," said Lotterer, a three-times Le Mans 24 Hours sportscar winner and, like Vergne, a former Formula One driver.
The one-two was the Chinese-owned Techeetah team's first in Formula E.
Rosenqvist, bidding for a third race win in a row, was fourth for Mahindra.
Brazil's defending champion Lucas di Grassi again hit problems and retired, failing to score for the fourth race in a row with Audi.
(Reporting by Alan Baldwin in London, editing by Clare Fallon)
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