Marquez picked up a problem as he was close to overtaking Baldassarri for second, running off track in Turn 1 in lap 15, with his rear brake disc glowing under the night sky.
Yamaha turned a corner in this area on Sunday afternoon in the warm-up session, according to Rossi, and this allowed him to stick with Andrea Dovizioso and Marc Marquez in race.
Andrea waited and stayed hidden; then, five laps from the end, he pulled the pin, snatching the lead from Zarco and taking command.
Behind these three were Jorge Lorenzo of Spain on the second factory Ducati at 0.470 sec off the pace and defending world champion and compatriot Marc Marquez on a Honda.
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Italian great Valentino Rossi will start his 23rd season of grand prix racing, at the age of 39, from eighth place for Yamaha.
It is the third time Dovizioso has beaten Marquez by snatching the lead on the final bend. Much like both of those races, Marquez waited until the final corner to attempt his pass, and again, much like the two previous races in 2017 it was an attempted block pass by the World Champion. This is the best way to start the season.
"It was a ideal race, flawless weekend", said Dovizioso.
The second Yamaha piloted by teammate Maverick Vinales turned out to be the slowest in 12th place, during second round of qualifying and finished 1.027s behind Zarco with a laptime of 1m54.707s.
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"Now, I will fully focus on the race and I hope to race without making mistakes during the 22 laps".
Rossi was happy with the podium and said the Yamaha was in good shape this year but he added they needed to do more to beat Ducati and Honda.
Maintaining his surprise pace until the end, Rossi crossed the line to complete the podium ahead of leading independent rider Cal Crutchlow on the LCR Honda. There is still a lot more that I need to learn in MotoGP. Andrea Iannone (Team Suzuki Ecstar) had a lonely Qatar GP in ninth position, ahead of Jack Miller (Alma Pramac Racing) who completed the top ten in his first race for his new team.
There was a sizeable gap between the top three and the rest of the pack, with Dovizioso's team-mate Jorge Lorenzo, who experienced a disrupted start to the session as he was forced to pit due to his GP18 sparking, nearly half a second down in fourth.
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