The measure still needs final approval, which could come by early December when council members vote on the city budget. If it passes, the benefits would go into effect in January.
Council member Jim Null, who had been undecided, said he voted in favor of the benefits because fairness required it.
"To deny benefits because of sexual preference is wrong. It is unconstitutional, and we should have learned that years ago with Amendment 2."
Amendment 2 was a statewide anti-gay-rights measure approved by voters in 1992 but overturned by the U.S. Supreme Court.
Councilwoman Sallie Clark, who voted against the benefits, said the plan borders on discrimination because partners of unmarried, heterosexual city workers are not eligible.
The city does offer benefits to common-law spouses.
The benefits are expected to cost $58,000 a year.
Aspen, Boulder, Denver, Glendale and Summit County also provide benefits for same-sex partners of employees.
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