The minority Welsh Assembly Government's £14.4bn budget has won the backing of AMs after a deal between the Labour administration and Plaid Cymru.
Ieuan Wyn Jones (L) held private talks with Rhodri Morgan
£9.6m more will go to schools and an extra £1.7m to services for children with special educational needs.
A £2m grant to help schools meet fuel bills is now promised every year rather than as a one-off.
Plaid said it had won a "major concession" but other opposition parties accused it of "caving in".
Plaid Cymru leader Ieuan Wyn Jones said the entire package amounted to an extra £13m for schools, although the Conservatives and Liberal Democrats argued that only £9m was new.
After a rowdy debate Plaid AMs, who form the largest opposition group, abstained in the vote, as did independent John Marek.
The other independent in the chamber, Trish Law, voted for the budget, helping Labour to win by 30 votes to 17, with 12 abstentions.
Mr Marek and Mrs Law said they did not oppose the budget because they had won important concessions for their constituencies.
Mr Jones said: "This is new money meaning no other budgets will be cut to provide the extra funds, which is a major concession from the government."
Assembly government Finance Minister Sue Essex said: "I'm not claiming that my budget today meets all the demands that have been made, that would have indeed been impossible, but it is a fair response that in my view meets the most urgent needs of people in Wales."
But Conservative assembly leader Nick Bourne said Plaid had allowed Labour to win a great victory.
He said: "The losers are schools, universities, and local authorities".
The Conservatives and Liberal Democrats accused Plaid Cymru of actually only gaining a tiny amount of extra cash for schools.
Liberal Democrat leader Mike German predicted Plaid's decision to let the budget pass could influence next May's assembly election.
He said: "They will go into the election as Labour's little helpers."
Hopes of a deal rose when Plaid Cymru last night invited ministers to negotiate directly with them, breaking with the rest of the opposition.
It is understood the deal was discussed by the Plaid group as a whole this morning before it was agreed with Labour.
This latest increase is on top of funding rises already announced.
Total education spending in Wales will increase by £383m next year, up by 24%.