The Belgian earned a first pole position in the series on Saturday, and maintained his composure to convert that into success in the Russian capital.
BMW driver Martin finished over four seconds ahead of team-mate Bruno Spengler, securing a third win of the season for the manufacturer.
However, Martin's comfortable triumph was not without its share of fortune.
A safety car on lap 23 threatened to bring the drivers that had started on the harder compound tyres into the fray.
But defending champion Mike Rockenfeller's crash with Adrien Tambay five laps later brought the safety car out for an elongated second stint, affording Martin the breathing room to cruise clear.
"It was a perfect day," Martin said. "First pole, first victory in my fifth race. I'm very happy."
Spengler enjoyed a quiet race to take second ahead of Audi's Mattias Ekstrom, who took advantage of Timo Glock's lack of pace in the final laps to prevent a clean sweep of the podium for BMW.
Glock ended the race in sixth behind team-mate Marco Wittmann and Audi's Nico Muller.
Wittmann leads the driver's standings by 20 points from Ekstrom, with Spengler nine points further back in third.