Dave Zabriskie, one of America's most accomplished cyclists, was involved in the crash and was forced out of the eight-day race with head and wrist injuries.
Race leader Levi Leipheimer was involved in a separate, massive crash at the start of the second finishing circuit through his hometown.
He finished more than one minute behind Brown but the five judges made a discretionary ruling and awarded the same finishing time to Leipheimer and the several-dozen riders in the accident.
Leipheimer, who won the prologue last year and again Sunday, maintained a one-second lead over first-year pro Jason Donald. Benjamin Jacques-Maynes was third overall, trailing by five seconds.
"No, I'm not surprised I still have the race lead," Leipheimer said. "You have to remember that circuits in races of this caliber aren't very common. But it's very necessary because of the crowds and amount of people on the course today, they deserve a show."
Brown, who rides for Dutch team Rabobank, completed the 97.1-mile (156.2 km) route from Sausalito in 4 hours, 17 minutes, 19 seconds.
The announcer initially called Greg Henderson of New Zealand as the stage winner, and Henderson thrust his fists into the air. The race was so close that it required a photo analysis that revealed Brown had won by four centimeters.
Allan Davis of Australia was third with the same time as Henderson.
Zabriskie won the opening stage of the 2005 Tour de France and led that race for several days. The accident-prone Zabriskie crashed in the fourth stage that year and left before the ninth stage due to injuries.
He finished second in the Tour of California last year and was the leading returning rider in the 144-cyclist field. Zabriskie went down in a solo crash Monday with about 30 miles (48 kms) remaining and withdrew.
Hospital officials said Monday evening that scans of Zabriskie's head and wrist showed no serious injury.
The second stage will be Tuesday with the 115.8-mile (186.3 km) Santa Rosa to Sacramento road race, reports AP.
The eight-day event continues through Sunday's stage seven circuit race in Long Beach. The winner earns US$15,000, plus various daily stage and bonus money, from a total purse of US$165,000.