The defending four-time champion, who started second on the grid, was helped again by Mercedes teammate Valtteri Bottas, who allowed him to overtake and then defended him from attack by title rival Sebastian Vettel of Ferrari, as he battled to finish second, AFP reported.
Russian President Vladimir Putin, who sat next to former F1 supremo Bernie Ecclestone after a late arrival at the Sochi Autodrom, saw the Briton make the most of Mercedes' strategy and a thrilling passing move on Vettel in what was an intriguing contest.
Bottas had started on pole and was unhappy at being asked to obey team orders that deprived him of a possible victory as he came home 2.5 seconds behind Hamilton, who looked sheepish about it all after the race.
Vettel finished third in the race and the German saw Hamilton extend his lead over him in the standings.
It was Hamilton's third win in Russia, his fifth in six races and the 70th of his career, confirming he has the momentum to clinch a fifth title triumph with five races remaining.
Kimi Raikkonen finished fourth for Ferrari ahead of Red Bull's Max Verstappen who marked his 21st birthday with a rousing drive, including a spell as race leader, from 19th on the grid.
Hamilton then went over to thank Bottas and commiserate. At the podium ceremonies, with Putin doing the honors, Hamilton maneuvered the Finn onto the top step alongside him.
“It’s actually quite a difficult day,” explained the Briton. “He was a real gentleman to let me by. Usually I’d be elated but I can understand how difficult it was for Valtteri.”
The Finn, without a win this season, had asked the team over the radio, more in hope than expectation, in the closing laps whether the order might change back.
“Is this how we are going to finish the race?” he asked, before the answer came back in the affirmative.
“Valtteri this is Toto. Difficult day for you and a difficult day for us,” said team boss Toto Wolff, whose finger had been captured by the world television feed hovering over the ‘tactics’ button before the order was given.
“Let’s discuss it afterwards when we come together and we’ll explain things.”