The Hawaii House gave the measure, which gives same-sex and heterosexual couples the same rights as married couples, final approval Thursday, the last day of the legislative session, on a 31-20 vote.
The vote came as lawmakers wrestled with the state budget deficit, The Honolulu Advertiser reported.
Lingle, a Republican, has until July 6 to decide whether to sign the measure, which fell short of the two-thirds majority necessary to override a possible veto.
Lt. Gov. James "Duke" Aiona said he would urge the governor to reject the measure.
"If the Legislature wanted to establish the equivalent of same-sex marriage, they should have put it on the ballot for the people to decide," Aiona said.
Hawaii's Supreme Court ruled in 1993 same-sex couples should be allowed to marry but voters adopted a constitutional amendment in 1998 that allowed the Legislature to define marriage as a union between a man and a woman.