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The Italian got back on his bike after a shake of his fist and resumed the race at the back of the field, but had to struggle on without a foot-rest and a broken brake lever.
"Elias caught me on the first bend after I'd made a great start, but he apologised and these things happen at the front," Rossi said after the race.
Capirossi, meanwhile, stormed off the front of the grid with Ducati team mate Sete Gibernau and Honda riders Hayden, Pedrosa and Melandri in pursuit.
Spain's Gibernau had to retire after what appeared to be an electrical problem with his bike on lap three.
Pedrosa, riding his first MotoGP race after stepping up from the 250cc class, broke clear of the chasing pack to set off in pursuit of Capirossi and gradually ate into the Italian's lead.
Capirossi, 12 years Pedrosa's senior, kept him at bay until 10 laps to go when the Spaniard reeled him in and tucked in behind the Ducati.
But the experienced Italian, a former 125cc and 250cc world champion, cranked up the pace with four laps to go to see off his younger rival.
The 130,000 fans at Jerez were given plenty more to cheer about earlier in the day with Spanish riders winning the opening two races.
Alvaro Bautista won his first ever grand prix in the 125cc race ahead of pole-sitter Lukas Pesek of the Czech Republic and Italy's Mattia Pasini.
Jorge Lorenzo followed up with his first victory in the 250s, crossing the line almost five seconds ahead of Alex de Angelis of San Marino and Italy's Andrea Dovizioso.