The 27-year-old, competing for the Virgin Racing team and starting third on the grid, was the first winner from the Netherlands in the five-season history of Formula E.
He was joined on the podium by Germans Andre Lotterer, for DS Techeetah, and Daniel Abt for Audi. Brazilian Lucas di Grassi was fourth for Audi.
Frijns now has 81 points to Lotterer's 80, with five rounds remaining.
"That was the hardest race of my life," said Frijns.
"If you're leading, the last thing you want is rain and everything was unpredictable. It was really difficult conditions. I'm just so happy to win this race."
The race started behind the safety car due to the damp conditions, with British driver Oliver Rowland on pole position for Nissan after Germany's Pascal Wehrlein was stripped of the top slot for incorrect tyre pressures.
Rowland crashed out soon after, handing the lead to Swiss team mate Sebastien Buemi who was then passed by Frijns after they had made contact on lap six.
Heavy rain and hail led to full course yellow conditions and a safety car period, with a temporary speed restriction of 50kph.
More crashes followed when the racing resumed, with former championship leader Jerome d'Ambrosio hitting the wall in the final minutes.
(Reporting by Alan Baldwin, editing by Clare Fallon and Ed Osmond)
