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A judge had agreed to waive the customary 24-hour waiting period on the women's marriage license before the weekend ceremony so that the couple could make it official the moment they said "I do" as the state law took effect.
Each had lobbied on behalf of gay marriage, with Lambert founding the local group OUTspoken For Equality in 2004.
More than 40 other gay couples will say "I do" during a joint ceremony at Niagara Falls on Monday.
New York City plans to open its marriage bureaus in all five boroughs on Sunday. Expecting lines around the block, city officials initially set a lottery capping the number of marriages to 764 couples, but later decided to accept all 823 applicants, gay and straight alike.
The expected rush of weddings across New York state has sent marriage bureaus scrambling for staff to officiate and judges to approve the marriages.
Dyster estimated that legalizing gay marriage would add some $400 million to the state's strained economy over the next three years.
Mayor Michael Bloomberg, who had pushed for same-sex marriage, is set to marry two men who belong to his City Hall inner circle at Gracie Mansion, the mayor's official residence, on Sunday evening.
Civil liberties activists in New York say the state's legalization of same-sex marriage sends a message to the US Congress that it must repeal the federal Defense of Marriage Act defining marriage as between a man and a woman and which excludes same-sex couples from federal benefits.