Britain's Lewis Hamilton dominated the Russian Grand Prix to take his ninth win of the year, his fourth in a row, and extend his championship lead.
Hamilton's team-mate Nico Rosberg fought back following a first-lap error to take second place, sealing the constructors' title for Mercedes.
Rosberg trails Hamilton by 17 points with three races remaining and a maximum of 100 points available.
Hamilton equalled Nigel Mansell's record for most wins by a Briton - 31.
The race was overshadowed by the sport's concern for Marussia driver Jules Bianchi, who is in a critical condition after a crash during the Japanese Grand Prix last weekend.
There was a tribute to the 25-year-old Frenchman on the grid from both his team and the other drivers.
Marussia decided to run only one car in the race, leaving Bianchi's fully prepared but on stands in the garage.
The race was attended by Russian President Vladimir Putin, who was instrumental in realising F1 boss Bernie Ecclestone's 30-year desire to have a grand prix in Russia.
Russia is paying a reputed $50m (£31m) a year for the race, believed to be the the largest hosting fee of any grand prix.
Unusually, Ecclestone stayed until the end of the race, sitting with Putin in the hospitality grandstand.
Putin then joined the drivers in the pre-podium room and on the podium, where he presented Hamilton with the winner's trophy and Mercedes executive director (technical) Paddy Lowe with that for winning constructor.
Hamilton had looked the superior of the drivers in the dominant Mercedes team throughout the weekend.
"Nico did a great job to recover," he said. "The car was performing really well. It's history for us. I feel very proud to be a part of it. To get the first constructors' championship for Mercedes-Benz is a wonderful day."
The only time Hamilton looked briefly vulnerable was when Rosberg pulled alongside him into the first proper corner, Turn Two.
But the German braked too late, badly locking up both front wheels and taking to the escape road.
Rosberg held on in front, but was immediately told to hand the place back to Hamilton because he had broken the rules by gaining an advantage through going off the track. He replied saying he would have to pit immediately to change his tyres.
He rejoined on the harder 'medium' tyre and proceeded to drive a measured race.
Rejoining at the back, Rosberg picked his way through the backmarkers and emerged in third place, right behind Valtteri Bottas, after the leading cars made their pit stops.
Rosberg then dived inside Bottas into Turn Two to move into second, and despite Williams's initial belief that Rosberg would run into tyre trouble, he was able to hang on without trouble to the end.
Rosberg, nearly 20 seconds behind Hamilton, put in a couple of quick laps to briefly close the gap a little, before Hamilton posted his own fastest lap to prove he was in total control.
His ninth win of the year means Rosberg, who has won four, can now not match his team-mate for victories in the remaining races.
But the championship fight is still wide open, helped by the award of double points in the final race in Abu Dhabi.
No matter what happens in the next race in the United States, Hamilton is mathematically unable to win the title until at least the Brazilian Grand Prix, the penultimate race of the season.
The title battle is now essentially down to the two Mercedes drivers as Red Bull's Daniel Ricciardo, in third place, is 92 points adrift of Hamilton.
Williams's Bottas was third in Sochi ahead of McLaren's Jenson Button.
The Englishman had been in a battle with Ferrari's Fernando Alonso, but the Spaniard dropped back behind the second McLaren of Kevin Magnussen with a slow pit stop.
Alonso fended off a challenge from Ricciardo in the later stages of the race to take sixth.
Bottas was unable to match the Mercedes but was out of reach of the McLarens, with Button again proving a more able race driver than Magnussen.
Behind Alonso and Ricciardo, the second Red Bull of Ferrari-bound Sebastian Vettel was eighth, ahead of Ferrari's Kimi Raikkonen and Force India's Sergio Perez.
Russian Daniil Kvyat, who qualified an impressive fifth, had a scrappy race and fell back to 14th at the finish.