City Councilwoman Rebecca Kaplan had introduced a resolution opposing the 3.2-mile connector, but at a lengthy hearing that ended at 1 a.m., the council rejected her motion and instead voted 5-0 to approve a substitute motion by Councilman Ignacio De La Fuente to endorse the controversial project.
Kaplan and Nancy Nadel abstained, and Desley Brooks was absent.
The project has already been approved by BART directors, the Metropolitan Transportation Commission and other agencies, so the City Council's vote was largely symbolic.
Project opponents, who include many public transit advocates who favor bus service over rail service, say BART could save hundreds of millions of dollars by using a rapid bus service instead. They estimated that such a service would only cost between $45 million and $60 million.
The conditions proposed by De La Fuente and endorsed by the City Council are that local workers be hired for constructing the rail connector, that an intermediate stop be built on Hegenberger Road and that an evaluation of the connector's fare rates be conducted to ensure that working people can afford to ride it.
Current plans call for a one-way ride on the connector to cost $6.
City Council President Jane Brunner said the conditions "are very important to me" because without them the connector mainly will benefit out-of-towners who go to the airport instead of Oakland residents.
The conditions authored by De La Fuente are similar to those suggested by Oakland Mayor Ron Dellums in a letter he issued to the council Tuesday afternoon in support of the project.
Dellums said he favors the connector because it "presents immediate economic opportunities for Oakland residents in dire need of jobs."
"As Oakland's mayor in a time when the city is facing unemployment rates of 17 percent, I cannot in good conscience turn away this prospect for our residents," Dellums said.