Reigning seven time MotoGP champion Rossi missed his home race after fracturing his lower right leg in a Saturday morning highside and could be sidelined for months.
Just before the start, Lorenzo held up a message for Fiat Yamaha team-mate Rossi saying "Everyone can feel pain, but not everyone can be a legend”, while the whole of the Ducati grandstand displayed the word “Vale” with red and white cards.
Rossi himself then gave a message via telephone from hospital, which wasbroadcast over the circuit PA system to the fans. Rossi, who was watching on TV (see separate story), said he missed everyone and would be back soon.
In Rossi's absence, Pedrosa converted pole into the race lead and simply rode into the distance, helped by nearest rivals Lorenzo and Dovizioso exchanging second place in the early stages.
Pedrosa's lead over the Lorenzo/Dovizioso battle reached eight seconds, before the Spaniard put his factory RCV into cruise control to claim his ninth MotoGPvictory by 4.014sec.
Lorenzo shook off Dovizioso in the closing stages to be the only rider to finish all four races this season on the podium, and the #99 now holds a 25 point lead over new nearest rival Pedrosa, with Rossi slipping to third.
Dovizioso at least had the honour of being top Italian and standing on his home podium, after his third third-place of the year.
On the podium, an unhappy Lorenzo - he later said he wanted to win to dedicate it to Rossi and couldn't understand his lack of pace - wore a “VR 46” t-shirt.
The fight for fourth was the only contest to stay alive to the flag, with Marco Melandri, Randy de Puniet and 2009 Mugello winner Casey Stoner trading places for much of the race.
Stoner secured fourth - his best result of the season - with a last lap pass on Melandri's Gresini Honda, while LCR Honda's de Puniet was left to settle for sixth, having led the group on the penultimate lap.
Ben Spies, who ran as high as fourth in the early laps, lost touch with the trio ahead on the final lap, but seventh place was just the kind of solid race he needed after failing to reach the flag in the past two events.
It will also do his chances of being called up to replace Rossi no harm at all, especially since Monster Yamaha Tech 3 tam-mate Colin Edwards - favourite for the temporary promotion - sunk back to 13th in the race.
Rossi is likely to be replaced by Catalunya at the latest, which follows Silverstoneand Assen on July 4.
Stoner was the only Ducati rider to finish after team-mate Nicky Hayden suffered his first DNF of the year, the American sliding out of sixth on lap six. Another Desmosedici rider, Mika Kallio, also failed to finish.
Behind Spies, the top ten was completed by Aleix Espargaro, Marco Simoncelli and Suzuki's Loris Capirossi.
Pramac's Espargaro claimed his best MotoGP finish, while Honda Gresini's Simoncelli charged through the field after running off track on the opening lap.
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