SACRAMENTO — In a dramatic victory for tenant advocates, the California Assembly narrowly passed a statewide rent-cap proposal on Wednesday night amid mounting pressure for lawmakers to protect renters from the steepest of increases in a hot rental market.

If the bill clears the Senate, California could become the second state in the nation this year to limit annual rent hikes, covering millions of properties not covered by local rent control rules.

In a final appeal to his colleagues, the bill’s author, Assemblyman David Chiu, said the bill would protect the most vulnerable residents who are a rent-hike away from eviction. “They are our neighbors,” he said. “They are our co-workers. They are our brothers and sisters. They are our grandparents.”

Assembly Bill 1482, which passed 43-28, would apply to most properties not covered by local rent control ordinances — including rented single-family homes and condos in cities with rent control. It was amended last week to exempt properties that are less than 10 years old, and — because of an 11th-hour handshake deal with a powerful trade group — it will undergo more key changes in the Senate.