Spanish rider Marquez, who won a record 13 races last season, clipped Rossi's back wheel and crashed out as Rossi raced on to victory from eighth on the grid.
"I'm sorry for the accident and sorry for him [Marquez], I hope he's ok," said Rossi. "I had a great race and the bike was fantastic, but I could see that he was having problems with his tyres," added the seven-time world champion.
Rossi also won in Qatar while Marquez won the second race of the campaign in Texas where the Italian came third.
Dovizioso on a Ducati came home second more than five seconds back with British rider Carl Crutchlow on a Honda third.
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