The vote was 108-50 on the resolution opposed by the United States, the European Union and Japan, who collectively pay 80% of the United Nations budget.
At the insistence of the US, the assembly in December tied progress on management reforms to approval of refinancing the UN budget on June 30.
The vote could well spur Washington and others to insist a budget cap stay in place and withhold the $950 million needed to pay UN salaries after June 30.
Separately, the United States could withhold its own dues, usually paid after September.
Kofi Annan last month introduced a 33-page blueprint on overhauling the bureaucracy, in part an outcome of scandals in the now-defunct Iraq oil-for-food programme.
He sought more financial oversight, simplified hiring and firing procedures, career planning, staff buyouts, a modern information system as well as flexibility in assigning staff and resources.
The wealthy nations do not want any final decision now on Annan's plans but prefer to wait for detailed reports he promised in May and June and then again in September.
However, they back Annan's proposal to give him more authority on where to spend funds and that a small, representative group of nations approve some of his choices and report back to the larger membership.
Dumisani Kumalo, South Africa’s ambassador to the UN and chairman of a group of 132 developing nations, said: "The report of the secretary-general had an unfortunate underlying theme - that is to change the role of oversight by the member states of the General Assembly."
Kumalo and others fear the General Assembly will lose control to the West over jobs and programmes they feel already favour wealthy nations.