The legislation - which still needs House approval - would divert $35 million in hotel taxes to buy land and upgrade infrastructure in Sandy for a $110 million soccer stadium.
RSL officials could not be immediately reached for comment.
Senate leaders thought they had smoothed the way for the bill, but it snagged briefly when some legislators asked for a night to sleep on the funding plan.
After a hasty closed meeting to line up the votes and make clear the money will not cut into funding for schools and roads, the Senate passed the tax-diversion bill and sent it to the House for debate.
Representatives are scheduled to consider the legislation Thursday.
Sponsoring Sen. Sheldon Killpack argued RSL provides a rare tourism opportunity for the state.
"Leisure dollars are very transient. They don't always stay put in the local market. And you don't have to look very far to find people trying to lure people from Utah," the Syracuse Republican said. "We've never flinched before at putting money to help with the image of the state."
And Cottonwood Heights Republican Sen. Carlene Walker, whose district includes the proposed Sandy stadium site, said Utah taxpayers should be comfortable with government oversight of the project.
"We as taxpayers, and particularly taxpayers in Salt Lake County have a great deal to gain," Walker said.
House members are expected to approve the bill.
Gov. Jon Huntsman Jr. applied the heat to lawmakers when he issued a news release earlier in the day, arguing state leaders are not using Utah taxpayers' money to build the stadium. "This is an economic-development investment in valuable property and a valuable community asset," he said.
"Real Salt Lake has become a proud part of our community and it is imperative for the Legislature to act now in order to keep this tremendous asset here in Utah," Huntsman said. "This project will enhance our quality of life, especially for the hundreds of thousands of Utah youth who play soccer."
Lawmakers had two options Tuesday: building a stadium in Sandy or moving the project to the State Fairpark in Salt Lake City.
Salt Lake City Mayor Rocky Anderson made a rare appearance on Capitol Hill on Tuesday to present his $12.5 million proposal to Democratic lawmakers.
"I think we're going to keep Real Salt Lake in the county one way or another," Anderson said. "I think we're going to make this happen."
If House members balk at the plan, Salt Lake City's site could take the forefront.
Some capital city representatives argued for the Fairpark because it would not divert tourism funding.
"I don't think this bill and the tax dollars we will be using is the right way to do that," said Sen. Ross Romero, a Democrat and self-declared soccer fan. "I'm frustrated that this is coming so fast at us because of a threatened impending sale."
But Romero was in the minority; the bill passed 20-8.
Meanwhile, Salt Lake County Council members approved a resolution earlier in the day in support of the Legislature's action.
The Sandy City Council is expected to restate its commitment to the project at a meeting tonight. Sandy Mayor Tom Dolan watched nervously from the Senate gallery.
"This has been out of my control for a long, long time," he said. "We appreciate the governor and the Legislature reconsidering it."
The Legislature must sign off on funding plan this week, Huntsman warned, to meet RSL's Friday deadline.
RSL owner Dave Checketts was in St. Louis today to discuss plans to lower ticket prices for his Blues National Hockey League franchise there. He also heard an offer from a group of investors interested in buying his Major League Soccer team and moving it to the Midwest.
Earlier on Tuesday, Jeff Cooper, the St. Louis-based attorney who is leading the investment group, reaffirmed that his group plans to make a "credible" offer to buy RSL.
Tribune reporter Michael C. Lewis contributed to this story.