Holeshot from pole
Marquez took the holeshot from pole as Dovizioso pounced for second, with Maverick Vinales (Monster Energy Yamaha MotoGP) losing out from the middle of the front row and Rossi leapfrogging his team-mate.
Marquez immediately pulled the pin to make a gap, with Rossi then soon attacking Dovizioso but the Ducati rider holding firm.
Miller on the move
Jack Miller (Pramac Racing) was next to go on the offensive as he dived past the ‘Doctor' but the move didn't stick, with Cal Crutchlow (LCR Honda Castrol) getting past Vinales to tag onto the Australian.
Chopping and changing, Danilo Petrucci (Mission Winnow Ducati) was next to attack the number 12 Yamaha in the melee - before Miller took Rossi, and Franco Morbidelli.
Dovizioso-Rossi battle
As the laps ticked on the Dovizioso-Rossi battle lit up and started to pull away from those behind.
Dovizioso blasted down the straights, Rossi made the most of the Yamaha's forte in the corners...the two trading positions at times.
Dovizioso in the hunt
As that raged on, the last lap was a relaxed one for Marquez. A block pass saw Rossi not only get past Dovizioso, but also create just enough of a gap to keep him ahead until the end.
Dovizioso, meanwhile, although forced to settle for third, achieved his goal of getting on the podium at a track that usually proved tough for Ducati - and he's only four points off Marquez in the Championship.
Marquez territory
Now it's time for chapter three at the Circuit of the Americas, traditionally Marquez territory.
Can he rule the venue once again and increase his lead? Find out on April 14 for the Red Bull Grand Prix of the Americas.