After retiring from race one, the Russian held off challenges from Nyck de Vries and Norman Nato to take victory, with Stoffel Vandoorne coming fourth to retain his championship lead, 11 points clear of Kvyat.
Vandoorne had won the first race of the meet, coming in ahead of Mikko Pakari and Jordan King, both of whom completed maiden podium finishes.
Koiranen Motorsport driver Kvyat had set a Formula Renault 2.0 lap record of one minute 42.261 seconds in qualifying to start on pole for the second time this season, alongside De Vries of R-Ace GP.
Kyvat had to hold off a strong challenge from De Vries but held out to the finish, more than making up for Saturday’s relative failure.
“Yesterday, after my retirement, my team was fantastic,” he said afterwards. “They picked me back up, and it’s thanks to them that I won today.
“We had no choice – I needed this victory. The gap between me and Stoffel is slim, and it’s impossible to call. We’ll have to fight to the end. I’m going to do everything I can to win the title.”