Mercedes extended its winning streak at the 5.848-kilometer Sochi Autodrom to six triumphs in as many races, since the return of the Russian GP to the F1 calendar in 2014, Efe news reported.
"It's incredible to have this result today given how fast (Ferrari) were off the start. It was hard just to keep up," Hamilton said after the race.
Mercedes' Fin driver, Valtteri Bottas, came in second, a spot ahead of Ferrari's other driver Charles Leclerc who completed the podium despite starting the race from pole.
Five-time world champion Sebastian Vettel (Ferrari), who started the race from P3 behind Hamilton, had to retire from the race in lap 28 due to a mechanical issue that came up just after his pit stop.
It was an unlikely one-two win for Mercedes this year in Sochi, as the German team's two drivers were not in the lead in the early going of the race nor Saturday's qualification.
It was the Ferrari duo who took the lead since the opening lap, with Vettel in first spot and Leclerc in second, ahead of Hamilton and Bottas.
At the outset it looked like the Scuderia was going to achieve the Italian team's fourth successive F1 race this one season, a rare event indeed.
But Vettel's retirement came in a moment that was useful for Mercedes racers, as Leclerc had been blocked from behind the safety car that has been deployed as Williams' George Russell had hit the barriers.
Then Hamilton and Bottas, who also were getting out from the boxes, jumped to first and second spots, respectively, and managed to hold their team's lead until the chequered flag was waved.
"I just had to keep Charles behind and just managed to do it so not bad," Bottas said following the race.
"We believed we could do it, we need to raise our game in qualifying but race pace is good."
Leclerc seemed frustrated again about his team's strategy, saying: "The tactic was me giving the slip steam so we were one-two at the end of the straight, but I don't know - I need to talk to my team about it."
Red Bull's drivers, Max Verstappen and Alexander Albon, finished the Russian GP in fourth and fifth spots, respectively, while Carlos Sainz (McLaren) came in sixth place.
Sergio Perez (Racing Point), Lando Norris (McLaren), Kevin Magnussen (Haas) and Nico Hulkenberg (Renault) completed the top-10 finishers list.
( With inputs from IANS )