SACRAMENTO — A controversial bill that abolishes “personal belief exemptions” for vaccinations won overwhelming approval in the California Senate on Thursday, bolstering supporters’ hopes that it will also clear the Assembly and be signed into law.

The measure by Democratic Sens. Richard Pan, of Sacramento, and Ben Allen, of Santa Monica — introduced after a outbreak of measles in December at Disneyland sickened 136 Californians — passed 25-10 after the two senators agreed to compromises aimed at easing its passage.

“Vaccines are necessary to protect us. That protection has been eroding,” Pan, a pediatrician, said in appealing for passage. “The science is clear: Vaccines are safe and efficacious.”

The measure, SB 277, would require children to be vaccinated before entering kindergarten. Medical exemptions are permitted, but exemptions based on personal and religious objections are not. That would make California one of only three states — the others are Mississippi and West Virginia — that doesn’t allow personal or religious exemptions to vaccine laws.

In a compromise, the authors agreed to limit the number of required vaccines to 10 to address critics’ concerns of an ever-expanding list of shots. They also amended their bill to remove a requirement for schools to notify parents of immunization rates. That made it possible for SB277 to bypass the Senate Appropriations Committee.

But perhaps the most significant compromise was the authors’ pledge to “grandfather in” many public and private school students whose parents have claimed personal belief exemptions. That would mean that more than 13,000 children who have had no vaccinations by first grade won’t have to get their shots until they enter seventh grade. And nearly 10,000 seventh-graders who today aren’t fully vaccinated may be able to avoid future shots because the state does not always require them after that grade.

The move was aimed at mollifying hundreds of angry California parents who have staged rallies and jammed hearing rooms, citing their concerns over vaccine side effects and asserting their parental rights.

“By scaling back the bill’s reach, their chance of success becomes much greater,” said Dan Schnur, director of the University of Southern California’s Unruh Institute of Politics.

Shannan Martinez, a spokeswoman for Pan, said Thursday the bill had not yet been amended to reflect the grandfather clause but that language will be written into the bill if attorneys agree that clarification is necessary.

Gov. Jerry Brown has signaled that he supports the bill, but there’s still a possibility he might urge legislators to include a religious exemption.

“I would be surprised if he didn’t sign it, because of the public health issues involved,” said Jack Pitney, a politics and government professor at Claremont McKenna College. “I think the governor, on one hand, is sensitive to parental rights, but also sees public health as a major responsibility of his.

“The anti-vaccine folks are going to make a very hard push, but passage in the Senate is a good sign it will become law,” Pitney said. “Sen. Pan made changes that made it more acceptable to some of the critics and that should greatly improve its changes in the Assembly.”

Most Republicans — including Sen. Patricia C. Bates of San Juan Capistrano, Sen. Mike Morrell of Rancho Cucamonga, Sen. Joel Anderson of San Diego and Senate GOP leader Bob Huff of Diamond Bar — voted against the measure.

“I am concerned about opportunities for equal education,” because unvaccinated kindergarteners would require home schooling, Bates said. “We have 3- and 4-year-olds in the state that are anticipating their first day of kindergarten.”

Added Morrell: “It tells deeply devout families that the government thinks it knows better.”

But Thursday’s vote and debate often crossed party lines, with Sen. Jeff Stone, R-Temecula, endorsing the bill from his experience as a practicing pharmacist and denouncing what he said were myths that have led to false concerns.

Sen. Richard Roth, D-Riverside, was one of two Democrats voting no. He still had concerns about the list of mandated vaccines. “I’m not sure there was a full explanation,” he said.

Outside the Senate chamber, a group of vaccine opponents from the California Coalition for Health Choice thanked senators who voted no as they left. They said they would step up efforts in the Assembly to highlight the impact SB 277 would have on schools and the difficulty of acquiring a medical exemption for immunizations.

“The only thing we can do is continue to educate our officials” about the personal belief exemption, said Lisa Bakshi, a mother from Placer County. “The parents who do it now do it for very legitimate reasons. We don’t do it because we are uninformed.”

The Associated Press and Sacramento Bee contributed to this report. Contact Lisa M. Krieger at 650-492-4098. Follow her at Twitter.com/Lisa M. Krieger.