With about 72 percent of the expected vote counted Thursday in unofficial returns, Referendum 71 was leading 52 percent to 48 percent, with a margin of about 60,000 votes.
Sen. Ed Murray, a Seattle Democrat who spearheaded the law, called it "a great step forward for equality in Washington state."
"I'm relieved," he said. "I was very concerned that if the voters had said no, it would have been a major setback for gay and lesbian families in Washington state."
The measure asked voters to approve or reject the latest expansion of the state's domestic partnership law, granting registered domestic partners additional state rights previously given only to married couples.
Full-fledged gay marriage is still not allowed under Washington law.
Gary Randall of Protect Marriage Washington, which opposed the law and pushed to get the referendum on the ballot, said they weren't ready to concede.
"We're just going to wait and watch it play out," he said.
Randall said that while they're waiting until all the votes are counted, "going in, we knew that we had a pretty tough task ahead of us."
"We knew there was a chance we would not prevail," he said.
Two national gay rights groups - the National Gay and Lesbian Task Force and the Family Equality Council - say that voter approval of such a measure was a first. Gay equality laws in other states, ranging from civil rights to gay marriage, have either been implemented by the courts or legislative process. Voters have rejected gay marriage 31 states, most recently in Maine, where voters repealed a gay marriage law on Tuesday.
"Our state made history today," said Anne Levinson, chairwoman of Washington Families Standing Together, which fought to keep the law on the books. "This is a day for which we can all look back with pride."
The expanded law in Washington state adds benefits, such as the right to use sick leave to care for a domestic partner, and rights related to adoption, child custody and child support.
During the campaign, opponents argued the law is a stepping-stone to gay marriage. Gay rights activists countered that while the marriage debate was for another day, same-sex couples need additional legal protections and rights in the meantime.
The law was to take effect July 26, but was delayed because of the referendum campaign. It will now take effect Dec. 3, according to the secretary of state's office.
The underlying domestic partnership law, which the Legislature passed in 2007, provided hospital visitation rights, the ability to authorize autopsies and organ donations, and inheritance rights when there is no will.
Last year, lawmakers expanded the law to give domestic partners standing under laws covering probate and trusts, community property and guardianship.
More than 12,000 people in Washington state are registered as domestic partners, and most are gay. Under state law, senior heterosexual couples can register as domestic partners as well, if at least one partner is 62 years old or older. That provision was included by lawmakers to help seniors who don't remarry out of fear they could lose certain pension or social security benefits.
Washington state, along with California, Oregon, New Jersey, and the District of Columbia, have laws that either recognize civil unions or domestic partnerships that afford same-sex couples similar rights to marriage.
Same-sex marriage is legal in Massachusetts, Connecticut, Iowa and Vermont, and will start in New Hampshire in January. Voters in Maine on Tuesday repealed a gay marriage law that was passed by the Legislature there earlier this year.
Gov. Chris Gregoire said that the vote on R-71 made her "very proud."
"I think Washington state stood out in this country on Tuesday by saying one of the inherent values in our state is equality," she said Thursday.
Results weren't known until Thursday because almost all voters in Washington cast their ballots by mail, and even those ballots postmarked on Election Day are valid. That means close elections often drag on for a few days or longer.