"We are called to live our faith, not legislate our faith ...," Moss said. "It's the charge of civil leaders to ensure that everyone is treated equally."
Advocates also argued that the bill would help eliminate discrimination against children of same-sex couples.
But opponents say the plan steps on people's religious freedoms. They argue lawmakers don't have the right to redefine marriage.
Committee members, noting their fatigue after a day of intense debate over guns, cast their votes on the marriage matter after an unusually brief debate on a polarizing issue.
The Senate approved the measure on Valentine's Day with Democratic support and a lone Republican tally by Champaign Sen. Jason Barickman.