The Russian started 13th and managed to finish the race in first place.
Second place was taken by his Italian teammate Luca Giotto.
The three prize-winners were closed by Swiss Louis Deletraz from Charouz Racing System.
Russian Artem Markelov from BWT HWA Racelab finished eighth.
Robert Schwartzman of Prema retired.
The second race will take place on 13 August.
Earlier it was reported that Lewis Hamilton won the qualification for the Tuscany Grand Prix.