It also provided Villaraigosa and Chiang an opportunity to take shots at Newsom, who has taken on front-runner status in the race.
The two pushed Newsom and former State Superintendent Eastin to provide more details on how to pay for a single-payer plan.
Estimates show that $50-$100 billion in new spending would be needed to run the system in California, possibly through an increased payroll tax.
"You gotta have a plan," said Villaraigosa, the former mayor of Los Angeles. "Anybody that is telling you we should do it without a plan is selling you snake oil.”
Appearing with the four Democrats on stage for the first time, Republicans Cox and Allen dismissed the idea of handing over control of health care to the government.
They focused much of their energy on attacking each others' conservative credentials, perhaps sensing that the only way to advance beyond the June primary is by consolidating the shrinking electorate of right-wing Californians.
As boos rained down from the Bovard Auditorium crowd, both Republicans defended President Donald Trump's immigration policies.
"The President is trying to work with Congress to get problems solved," said Allen, a State Assemblyman from Orange County.
They also sparred over their dueling efforts to repeal California's new gas tax. A twelve cent increase at the pump went into effect last November, in order to fund road repair and infrastructure projects in the state.
Allen appeared to admit the failure of his own repeal measure, when he encouraged the audience to support a separate repeal push backed by Cox, a San Diego businessman.
"Travis, welcome to the fight on repealing the gas tax," Cox quipped.
Saturday's debate may have also provided a preview of future attacks by Democrats on Newsom, who led the field in fundraising and every gubernatorial poll last year.
State Treasurer Chiang and Villaraigosa brought up studies that have found large gaps in the test results of African-American and white students in San Francisco, where Newsom served as mayor.