The Welsh assembly has said variable student tuition fees "are, in principle, wrong".
A decision has not yet been made on future fees in Wales
The Liberal Democrat amendment was passed by 31 votes to 27.
One member of the Welsh cabinet - economic development minister Andrew Davies - accidentally voted for the amendment.
The main assembly government resolution delegating to the first minister a decision on introducing variable fees was also approved.
The Liberal Democrats had also sought to ensure that the decision should rest with the whole assembly, but this was defeated.
Their education spokesman, Peter Black, said: "What is clear is that the future of students in Welsh higher education institutions will not be safe in the hands of this assembly government."
'Words of advice'
The Westminster government plans to introduce variable university tuition fees for England from 2006.
Its Higher Education Act devolves power over fees to the Welsh Assembly Government, which has promised not to use that power before 2007.
The formal transfer of the power lay behind the series of votes in Cardiff on Tuesday.
A Labour backbencher, Peter Law, voted - intentionally - against his party whip.
He said that, while the main motion simply devolved the decision, "it didn't hurt for us to underline a few words of advice on the way through".
"What I am saying is to you now is that the young people of tomorrow and students generally have great expectations of the government because only we can change this tax on learning.
"That's the challenge to the first minister."
Plaid Cymru spokeswoman Janet Ryder said there was "considerable confusion" over the policy.
She asked Education Minister Jane Davidson to clarify whether students starting courses in 2006 would have to pay higher fees for their second and third years.
Ms Davidson said the assembly government would keep its manifesto commitment - not to introduce top-up fees in this assembly term, which ends in April 2007.
In a statement later, she added: "The assembly government will be considering the implications of the motion passed today."
She had already made it clear, she said, decisions on the future fee regime in Wales would be taken in the light of an independent inquiry.
"In considering those recommendations and bringing proposals forward, we will need to take account of the needs of students and of institutions and of course have regard to the views of this assembly," Ms Davidson said.
The National Union of Students said it wanted to thank all the assembly members who had voted in favour of the Liberal Democrat amendment.
It was a positive reflection of the assembly's empathy with students, who would be demonstrating in Cardiff on 2 December against the introduction of variable fees in Wales.
The president of NUS Wales, James Knight, said: "It is great to see devolution being used in such a positive way. We are extremely pleased that the assembly have concluded that introducing a market into higher education is wrong in principle."
The union's UK president, Kat Fletcher, said: "This news is the first positive step on the long road to a free education for all.
"But NUS will not rest until every student receives the funds they need to study without having to work or live in hardship. The fight goes on."