ALBANY — Lawmakers voted late Friday to legalize same-sex marriage, making New York the largest state where gay and lesbian couples will be able to wed, and giving the national gay-rights movement new momentum from the state where it was born.

The same-sex marriage bill was approved on a 33-to-29 vote, as 4 Republican state senators joined 29 Democrats in voting for the bill. The Senate galleries were so packed with supporters and opponents that the fire marshals closed them off. And along the Great Western Staircase, outside the Senate chamber, about 100 demonstrators chanted and waved placards throughout the night — separated by a generation, a phalanx of state troopers and 10 feet of red marble.

“Support traditional marriage,” read signs held by opponents. “Love is love, Vote Yes,” declared those in the hands of the far more youthful group of people who supported it.

Senate approval was the final hurdle for the same-sex marriage legislation, which is strongly supported by Gov. Andrew M. Cuomo and was approved last week by the Assembly. Mr. Cuomo is expected to sign the measure soon, and the law will go into effect 30 days later, meaning that same-sex couples could begin marrying in New York by midsummer.

Passage of same-sex marriage here followed a daunting run of defeats in other states where voters barred same-sex marriage by legislative action, constitutional amendment or referendum. Just five states currently permit same-sex marriage: Connecticut, Iowa, Massachusetts, New Hampshire and Vermont, as well as the District of Columbia.

The approval of same-sex marriage represented a reversal of fortune for gay-rights advocates, who just two years ago suffered a humiliating, and unexpected, defeat when a same-sex marriage bill was easily defeated in the Senate, which was then controlled by Democrats. This year, with the Senate controlled by Republicans, the odds against passage of same-sex marriage appeared long.

But the unexpected victory had an unlikely champion: Mr. Cuomo, a Democrat who pledged last year to support same-sex marriage but whose early months in office were dominated by intense battles with lawmakers and some labor unions over spending cuts.

Mr. Cuomo made same-sex marriage one of his top priorities for the year and deployed his top aide to coordinate the efforts of a half-dozen local gay-rights organizations whose feuding and disorganization had in part been blamed for the 2009 defeat. The new coalition of same-sex marriage supporters also brought in one of Mr. Cuomo’s trusted campaign operatives to supervise a $3 million television and radio campaign aimed at persuading a handful of Republican and Democratic senators to drop their opposition and support same-sex marriage.

For Senate Republicans, even bringing the measure to the floor was a freighted decision. Most of the Republicans firmly oppose same-sex marriage on moral grounds, and many of them also had political concerns, fearing that allowing same-sex marriage to pass on their watch would embitter conservative voters and cost the Republican Party its one-seat majority in the Senate. Leaders of the state’s Conservative Party — the support of which many Republican lawmakers depend on to win election — warned that they would oppose in legislative elections next year any Republican senator who voted for same-sex marriage.

But after days of agonized discussion capped by a marathon nine-hour, closed-door debate on Friday, Republicans came to a fateful decision. The full Senate would be allowed to vote on same-sex marriage, the majority leader, Dean G. Skelos, said Friday afternoon, and each member would be left to vote according to his conscience.

"The days of just bottling up things, and using these as excuses not to have votes — as far as I’m concerned as leader, its over with," said Mr. Skelos, a Long Island Republican.

Several senators delivered impassioned speeches about the vote.

The lone Democratic opponent, Senator Ruben Diaz of the Bronx, said it was “unbelievable” that the Republican Party, “the party that always defended family values,” had allowed same-sex marriage to pass.

“God, not Albany, has settled the definition of marriage, a long time ago,” he said.

But Mark Grisanti, a Buffalo Republican who opposed gay marriage when he ran for election last year, said he had studied the issue closely, agonized over his responsibility as a lawmaker, and concluded he could not vote against the bill. Mr. Grisanti voted yes.

“A man can be wiser today than yesterday, but there can be no respect for that man if he has failed to do his duty," Mr. Grisanti told his colleagues.

The tide of change in Albany began as Mr. Cuomo relentlessly pressed lawmakers in a series of phone calls and sit-down meetings, advocates also tried to demonstrate shifting public opinion, citing polls that showed a majority of New York voters supporting same-sex marriage, and releasing almost daily written or videotaped expressions of support from celebrities as well as professional athletes, business leaders, and political figures.

The legalization of same-sex marriage in the United States is a relatively recent goal of the gay-rights movement, but over the last few years, gay-rights organizers have placed it at the center of their agenda, steering money and muscle into dozens of state capitals in an often uphill effort to persuade lawmakers.

In New York, passage of the bill reflects rapidly evolving sentiment about same-sex unions. In 2004, according to the Quinnipiac poll, 37 percent of the state’s residents supported allowing same-sex couples to wed. This year, 58 percent of them did. Advocates moved aggressively this year to capitalize on that shift, flooding the district offices of wavering lawmakers with phone calls, e-mails and signed postcards from constituents who favored same-sex marriage, sometimes in bundles that numbered in the thousands.

Dozens more states have laws or constitutional amendments banning same-sex marriage, many of them approved in the last few years, as same-sex marriage moved to the front line of the culture war and politicians deployed the issue as a tool for energizing their base.

But New York could be a shift: It is now by far the largest state to grant legal recognition to same-sex weddings, and one that is home to a large, visible and politically influential gay community. Supporters of the measure described the victory in New York as especially symbolic — and poignant — because of its rich place in the history of gay rights: the movement’s foundational moment, in June of 1969, was a riot against police inside the Stonewall Inn, a bar in the West Village.

     On Friday night, as the Senate voted, a crowd jammed into the Stonewall Inn, where televisions were tuned to the Senate hours before the vote began.  Danny Garvin, 62, said he had been at the bar the night of the riot, and came back to watch the Senate debate Friday. On the streets where police beat gay men in 1969, on Friday crowds cheered, as police quietly stood watch. Bernie Janelle, 53, turned to her partner of 16 years, Cindy Hearing, and said, “I’m going to propose to her on Sunday.”

Just before the Senate’s marriage vote, lawmakers in the Senate and Assembly also approved a broad package of major legislation that constituted the remainder of their agenda for the year. The bills included a cap on local property tax increases, and a strengthening of New York’s rent regulation laws, as well as a five-year tuition increase at the State University of New York and the City University of New York.

After passing the marriage measure, the Legislature was expected to adjourn its annual legislative session, which had been scheduled to end June 20.