The legislation, which now goes to the Assembly, is part of a broader package of bills designed to create jobs.
Senate President Pro Tem Darrell Steinberg, a Democrat, says furloughing employees at agencies that collect taxes is costing the state hundreds of millions of dollars annually in lost revenue.
His bill also would exempt employees at agencies that receive most of their budgets from fees or the federal government. Those include the Department of Motor Vehicles, where customers have seen their wait times increase since furloughs began last year.
The bill was approved on a 30-6 vote Thursday and would end furloughs for 80,000 state employees.