The party-line vote was 8-5.
The Assembly budget panel OK'd the measure 8-4.
Final adoption is expected this week.
Democrats rejected the budget Republican Gov. Chris Christie proposed and drafted their own version.
The Democrats' proposal adds funding for public education, cities and towns experiencing crime spikes and property tax relief for seniors who own homes.
It's about $1 billion higher than Christie's spending plan.
Democrats separately are proposing to reinstate a two-year surcharge on millionaires.
Christie has vowed to veto the tax increase.
A balanced budget must be in place by July 1, or the state technically runs out of money and the government shuts down.