Fifth for Capirossi matched Rizla Suzuki's best of the year so far, while Elias slipped back to sixth after his early heroics.
Mika Kallio's third and final scheduled race of the year for Ducati Marlboro ended with a MotoGP best of seventh.
Team-mate Nicky Hayden, who had predicted some 'drama' through the opening corners, was an innocent victim of a clash between Colin Edwards and Alex de Angelis - the Sammarinese hitting Edwards broadside at turn two, with the impact in turn clipping the back of Lorenzo's bike before bringing down Hayden.
Hayden made his feelings clear to de Angelis, who went from hero to zero after his Indy podium and was labelled by Edwards as a 'dumb Italian'. Edwards has now lost fifth in the championship to Dovizioso.
Completing the top ten behind Kallio was Marco Melandri (Hayate), Chris Vermeulen (Suzuki) and James Toseland (Tech 3).
Aleix Espargaro, subbing for Kallio at Pramac Ducati, finished his second MotoGP in an impressive eleventh, ahead of Randy de Puniet (LCR Honda), his team-mate Niccolo Canepa and Scot Honda's Gabor Talmacsi.
With the planned Hungarian round postponed for a year, round 14 of the 2009 MotoGP World Championship will be held at Estoril on October 4, when Stoner is scheduled to return from a three-race hiatus caused by fatigue problems.
San Marino Grand Prix:
12. de Puniet