With Marquez's Honda team pitting the reigning champion with 10 laps remaining, Rossi and Lorenzo -- who had started on pole -- stayed out.
Lorenzo came in with eight laps to go but his hopes vanished when he crashed on the next lap just as Rossi, who ended up fifth, was brought in for his switch back to slick tyres.
For the first time since the days of Barry Sheene in 1979, two British riders stood on the podium in the top category with Bradley Smith second on a Tech3 Yamaha and Scott Redding third for Marc VDS Honda.
Rossi has 247 points to Lorenzo's 224, with Marquez on 184 after his fourth win of the season and 23rd of his career. There are five races left with Spain's MotorLand Aragon hosting the next one on Sept. 27.
"The championship is a lot more important that winning this race, it‘s the main target," said Rossi, who had hoped for much more in the race closest to his home.
"It was a crazy race and when you have to change the bike, in this case twice, you need luck and rapid thinking to understand the situation."
Lorenzo cursed his misfortune.
"I think I‘ve been unlucky this year in general, but especially these last two races because I could have won both or finished second, but that‘s racing," said the Spaniard.
"In previous years, my rivals in the championship crashed and this year it‘s me who‘s unlucky, but all is not lost."
Smith reaped the reward for staying on slick tyres during the rain shower and coming through from 19th.
"I just kept telling myself ‘luck favours the brave'," said the Briton.
Scott Redding's first MotoGP podium was even more remarkable after he went into the gravel on the seventh lap.
"The marshalls tried to hold me back but I was fighting to get on the track. It was an incredible race and the adrenalin was through the roof," he said.
(Reporting by Alan Baldwin in London, editing by Clare Fallon and Pritha Sarkar)
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