A bill that would impose a statewide rent cap and restrict evictions moved forward Tuesday, marking a victory for advocates who so far have been struggling to pass legislation aimed at easing the state’s housing crisis.

Assembly Bill 1482, which would restrict rent increases on certain properties to an average of about 10 percent a year and prevent landlords from evicting tenants with no cause, passed out of its first Senate committee hearing late Tuesday. That signals a win for housing and tenants’ rights advocates, who have been trying to push a package of housing-related bills through the legislature, but have watched in dismay as several have been killed or watered down along the way.

“As our homelessness crisis worsens, it is crucial we take steps to keep families in their homes,” the bill’s author, Assemblyman David Chiu, D-San Francisco, wrote in an emailed statement. “This legislation will protect renters from egregious rent increases and predatory evictions while still allowing landlords to turn a profit. Today’s vote shows there is strong momentum in the legislature for increasing protections for California renters.”

His bill had secured four votes in the Senate Judiciary Committee as of Tuesday afternoon and picked up the last vote needed later in the day as committee members who had been absent during the initial vote weighed in. Dozens of supporters and opponents lined up to comment on the measure, which has received fierce opposition from landlord interest groups.

“Our biggest concern has always been that we don’t make a bad problem worse by scaring off development in California,” said Debra Carlton, spokeswoman for the California Apartment Association. “We want balance and we want stability.”

Despite recent changes that limit the impact of the controversial rent cap bill, researchers say the proposed law still would affect millions of California households. AB 1482 could impact as many as 4.6 million homes throughout the state that aren’t already under rent control, according to a recent study by UC Berkeley’s Terner Center for Housing Innovation.

“From the perspective of the number of new units and renters covered, I think the impact could be pretty substantial,” said David Garcia, policy director for the Terner Center.

That impact largely would be felt in cities that have no rent control policies, such as Palo Alto and Concord. In cities that already have rent control, the bill would extend protections to households that had been exempt under state law — including some single-family homes and apartments built after 1995 (or later in some cities) but not within the past 10 years.

Chiu put several limits on AB 1482 in the hopes of making it more palatable to the opposition. In addition to only covering rental units that are 10 years old or older, the bill would sunset after three years and landlords who own 10 or fewer single-family homes would be exempt. That last provision not only greatly reduces the impact the bill would have on single-family homes, but it also makes that impact hard to quantify, the Terner Center researchers wrote. Almost 2 million of the estimated 4.6 million California homes that will be covered by the rent cap are single-family homes, but there is no way to reliably estimate how many of those single-family homes are owned by landlords with more than 10 properties, according to the report.

The California Apartment Association seized on that limitation in its criticism of the Terner Center report.

“Over and over, the authors of the Terner Center report announce the limitations of their data,” spokesman Joshua Howard wrote in an emailed statement. “That makes it difficult for us to trust the conclusions in the report.”

In the Fruitvale and West Oakland neighborhoods of Oakland — both historically low-income neighborhoods that are rapidly gentrifying — the bill could bring rent-hike protections to 9,381 apartments and 6,827 single-family homes not currently covered by rent control, according to the Terner Center report. Oakland’s existing rent control rules apply only to apartments built before 1983.

In San Francisco’s Mission district, 10,984 apartments that currently don’t have rent control would be covered by the new rent cap, as well as 2,258 single-family homes. San Francisco’s existing rent control rules apply only to apartments built before 1979.

The researchers did not break out data for any South Bay or Peninsula cities.

AB 1482 now heads to the Senate Appropriations Committee, and then potentially onto the Senate floor. If it passes those votes, it will head back to the Assembly floor for a second vote to approve recent amendments. The bill is co-authored by Assemblymembers Rob Bonta, D-Oakland; Tim Grayson, D- Concord; and Buffy Wicks, D-Oakland.

Update: This story has been updated to reflect the bill’s passage out of committee after publication time.