At issue is an amendment to the California Constitution that bars this type of party involvement in nonpartisan races.
Detroit, for example, has elected its mayors and other officials in nonpartisan races since 1918.
Another councilman, Chris Bell, was running third with 16 percent of the votes in the nonpartisan race.
Mr. Hayden, a Democrat, joins a crowded field in the nonpartisan race.
Turnout was light in the three nonpartisan races.
It moved toward nonpartisan races in the early 1990's partly to cut the costs of conducting runoff elections, which resulted frequently from party primaries.
Polls indicate that the victor in the nonpartisan race will be Mr. Brown.
It supports candidates for the nonpartisan races in the city.
The nonpartisan race was so close that different exit polls conducted by Detroit's two daily newspapers pointed to different winners for much of the night.
Both men are Democrats in a nonpartisan race, and both are traditional liberals.