The bill, which passed in a 13-11 vote, needs to be signed by Governor John Lynch to make New Hampshire the fifth U.S. state where gay marriage is legal. The Democrat has not indicated whether he will sign or veto the bill, but has expressed opposition to the measure.
The bill passed the state's House of Representatives on March 26 but looked set for near certain defeat in the Senate before the amendment, which appeared to mollify some critics in the Democratic-controlled chamber.
The last-minute changes to the legislation would allow clergy to decline to marry homosexual couples and give couples the freedom to either keep the words "bride" and "groom" on marriage licenses, or use the word "spouse" instead.
Because the Senate and House passed separate versions, they must resolve their differences before the bill can go to the governor, who in 2007 signed a law recognizing same-sex civil unions, making New Hampshire the fourth state to do so.
Lynch has said the word marriage should be reserved for a traditional heterosexual relationship.
The bill, which would take effect on January 1, also recognizes out-of-state gay marriages and civil unions. Couples who now have civil unions would automatically become married by January 1, 2011. The extra year allows time for a formal ceremony.
Gay marriage made big inroads this month when, in a single week, Iowa and Vermont joined Massachusetts and Connecticut in allowing gay couples to legally wed. On Tuesday, a joint judiciary committee in neighboring Maine's legislature approved a bill to allow same-sex marriage. Maine's House and Senate could vote on the measure as early as next week.
In California, gay marriage advocates are hoping to overturn Proposition 8, the 2008 constitutional amendment that banned gay marriage there, in the state's highest court.
CULTURAL SHIFT
New Hampshire in 1987 outlawed same-sex marriages. In 2004, after Massachusetts' top court allowed gay couples to marry, New Hampshire passed a law that would not recognize gay marriages from out of state.
But elections in 2006 signaled big political and cultural changes, giving Democrats majorities in both chambers of the legislature for the first time since 1874 in a state that was long a stronghold of moderate Republicans.
New Hampshire state Senator Lou D'Allesandro was the only Democrat to side with 10 Republicans against the legislation, which would redefine marriage to include same-sex couples. He cited his "traditional family values."
Democratic state Senator Deborah Reynolds, who opposed the bill at committee level, changed her vote after the amendment.
"This is a compromise that is respectful to both sides of this debate and meets our shared goal of equality under state law for all the people of New Hampshire," Reynolds said.
Senate Republicans said discrimination remains in the bill, which Democrats said would ensure gay couples no longer received a "separate but equal" civil union distinction.
"Marriage for centuries has the traditional meaning of one man and one woman, and we believe that term should not be co-opted to be used for other purposes," said Republican Peter Bragdon, the Senate minority leader.