Having passed this first hurdle, the bill will now go on to be voted upon by the House of Representatives, next week.
"In a world where there are more tensions between people, our country has offered a loving embrace to its own", Senator Smith said.
"It says to so many Australians, this parliament, this country, accepts you for who you are", she said.
"Next week it heads to the House of Representatives", said the Equality Campaign, a group that supports the marriage bill, on its Twitter page.
Equality campaigners are expected to keep the champagne on ice following the passage of the landmark bill to legalise same sex marriage in the Senate.
Repeating a concern that he voiced several times during the senate debate, Senator Abetz said that Senator Smith's bill went further than most Australians realised because it would also allow transgender and intersex people to Wednesday. "It says you're one of us".
"Our relationships have existed for a long time". Our love is true. Our families are precious.
"We would like to see protections for freedom of speech, the freedom of religious schools to teach and act out their beliefs about marriage", he said.
Some conservatives had wanted to add an amendment that created two separate definitions of marriage, one for heterosexual couples and one for everyone, which was rejected.
Supporters of the same-sex marriage "Yes" vote celebrate in Sydney earlier this month.
Various amendments to the bill - including moves to allow civil celebrants to refuse to perform gay weddings - were defeated in the Senate on Tuesday and Wednesday by a combination of Labor, the Greens, some Coalition senators and some crossbenchers. The government has said the house will not adjourn until the legislation is passed.
'Today I am so proud of this country'.
The Tasmanian senator said that it should be remembered that religious rights are part of Australia's global obligations, while same sex marriage was not.
Parliamentarians from both sides had a conscience vote on the bill, and many chose to abstain - including Employment Minister Michaelia Cash, Assistant Social Services Minister Zed Seselja and One Nation leader Pauline Hanson.