But Sir Keir’s party reaffirmed its decision to cut the cash from older people despite the vote.
A Labour spokesman said: “The Tories wrecked our economy and left a £22 billion black hole in the public finances. They made commitments they couldn’t pay for, covered it up and ran away.
“The Labour Party was elected on our manifesto commitment to sound fiscal rules, economic growth is our primary mission and we will take the tough decisions now to rebuild Britain and make every part of the country better off.”
Winter fuel payments were previously available to everyone above state pension age.
But older people will now only receive it if they get pension credit.
The Treasury said the winter fuel changes would see the number of pensioners receiving the payments plummet from 11.4 million to 1.5 million.
Unite’s general secretary Sharon Graham received several rounds of applause when she made a powerful plea for the allowance to be restored at the conference yesterday (WED).
She said: “People simply do not understand, I do not understand, how our new Labour Government can cut the winter fuel allowance for pensioners and leave the super rich untouched.
“This is not what people voted for. It is the wrong decision and needs to be reversed.”
The motion passed narrowly with some disquiet at the decision in the room when some delegates felt it had gone the other way
Sir Keir was not present for a debate on the policy as he jetted to New York the night before to attend a United Nations summit.
Unions slammed Labour earlier this week for trying to “silence” pensioners and avoid humiliation by blocking the crunch vote which was scheduled for Monday.
It was then relegated to the “graveyard slot” of the conference when most people had left and all major political speeches finished.
Fran Heathcote, Public and Commercial Services Union general secretary, said: “Labour’s affiliated unions and party members sent a message to the Labour leadership that they have got this one wrong.
“Keir Starmer and Rachel Reeves should listen to pensioners, trade unions and their own party, and drop this unnecessary cut.
“They should also listen to themselves. Just before the election Labour attacked a Conservative minister who proposed cuts to Winter Fuel Payments and vowed they would “be on the side of pensioners let down by the Tories.”
Trust in politics is at an all-time low. Keir Starmer promised to restore honesty and integrity to Downing Street after years of scandal. He should be big enough to hold his hands up, admit he called this one wrong and change course. People would respect that candour.”
But Sir Keir refused four times to apologise for cutting winter fuel payments.
The Prime Minister was repeatedly pressed on the matter during an interview with Good Morning Britain but declined to say sorry.
Alan Tate, of the Communication Workers Union (CWU), said the winter fuel payment cut had “overshadowed” the work of the new Labour Government.
He said: “The CWU has been inundated with emails and calls from our retired members worried about choosing between heating and eating.”
Dozens of pensioners had gathered outside the venue on Monday to voice their anger at the Chancellor’s decision.
At least 1.6 million disabled people 70% of disabled pensioners previously receiving the winter fuel payment will lose it under the new rules.
Meanwhile around 800,000 older people are not claiming pension credit despite being eligible.
The government has worked with charities, local authorities and broadcasters to ensure as many of those eligible as possible receive the benefit and the winter fuel payment this winter.
The Government won a vote on the plan to restrict the payments to all but the poorest pensioners by 348 votes to 228 earlier this month – a majority of 120.
Fifty-two Labour MPs did not take part in the vote, including seven ministers, but it is unclear how many deliberately abstained or were absent from Parliament for another reason.
Only one Labour MP, Jon Trickett, voted against the government on what he said could “be a matter of life and death” for his constituents.
After yesterday’s vote, the former frontbencher added: “Unions and party delegates were not persuaded to vote for cuts to winter fuel allowance. The conference spoke for poorer pensioners.”