Former minister Frank Field said he was withdrawing a rebel amendment which had attracted the signatures of 45 Labour MPs and threatened Gordon Brown with his first Commons defeat as Prime Minister.
The move came after Mr Darling announced he would meet one of the rebels' key demands that compensation should be backdated to the start of this financial year, when the tax change comes into effect.
In a letter to the chairman of the Commons Treasury Select Committee, Mr Darling said that he would use the winter fuel payment system, tax credits and the minimum wage to help two groups thought most likely to lose out from the abolition of the 10p rate - low-income households without children and pensioners aged 60-64.
The announcement came just moments before Mr Brown's weekly appearance before MPs for Prime Minister's Questions in the Commons, which Conservative leader David Cameron quipped should be renamed "Prime Minister's U-turns".
Mr Field said: "The Chancellor's statement this morning is to be welcomed. He is actively seeking ways of compensating workers made worse off by the loss of the 10p starting rate of tax, either by changing personal allowances and tax codes or by changes to tax credits.
"It is terrific news for our constituents who earn modest wages and salaries and for Labour MPs who have been actively supporting their campaign
"The Government has listened, and more importantly acted upon what many Labour MPs have been saying, and I shall now be withdrawing the amendment to the Budget that stands in the name of nearly 50 Labour MPs."
Mr Darling's action came amid mounting pressure from Labour backbenchers worried about the impact of the abolition of the 10p rate, which was announced by Mr Brown in his final Budget as Chancellor last year and comes into effect this month.
Some 5.3 million people - many of them low-paid workers earning less than £18,000 a year - are expected to see a cut in their pay packet this month as a result.
In his letter to Mr McFall, the Chancellor spelt out how he intends to help those affected: "For pensioners aged 60-64, whose incomes tend to be more stable, we have put in hand work to see if those households who have lost out from the removal of the 10p starting rate of income tax can be helped through the mechanism that already exists to pay the Winter Fuel Allowance.
"As a sign of the Government's intent, we do not wish to wait unnecessarily until November. Whatever conclusions we come to, all the changes will be backdated to the start of this financial year.
"For other low-paid families currently outside the working tax credit system, while we will examine in our review all practical propositions, our focus is on potential changes to the tax credits system to allow the average losses from the removal of the 10p starting rate of income tax to be offset.
"At the same time, the Secretary of State for Business, Enterprise and Regulatory Reform (John Hutton) and I have asked the Low Pay Commission to report on what changes could be made to the minimum wage regime to support younger workers. We will look at other measures alongside this."
Mr Cameron described today's announcement as a "humiliating climbdown" designed to save the Prime Minister's skin and said Mr Brown had suffered "a massive loss of authority".
He told MPs: "Has the Prime Minister got any idea of what a pathetic figure he cuts today? He is making these changes because he thought he would lose the vote."
Quoting a string of Labour figures who have questioned the PM's handling of the affair, Mr Cameron asked: "Isn't it the case that the Labour Party have finally worked out that they have a loser, not a leader?"
But Mr Brown said the 10p rate was not the best way to boost the incomes of the poor, who had benefited from improvements in tax credits and the minimum wage under Labour.
"The central issue is that we have taken more people out of poverty than any previous Government," Mr Brown told the Commons.
"The choice is very clear - between a Conservative Party that would cut the incomes of the poor and a Labour Party that will increase them."
Labour will hope that today's concession will take the sting out of the tax row ahead of key elections to English and Welsh councils and the London mayoralty on May 1, when the party is widely expected to fare badly.
Details of the additional support to be offered will be published in Mr Darling's Pre-Budget Report in the autumn.
Meanwhile, the Treasury Select Committee will carry out its own investigation into the impact of the tax changes on Britain's poorest households, which report in July before MPs have their final chance to vote on the Finance Bill.
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