The government's majority was cut to just 20 as the Conservatives lost a bid to prevent the planned closure of 2,500 sub-post offices.
Mr Hutton said technology had changed the role of the Post Office
A vote to suspend the closure was defeated by 268 to 288. At least 19 Labour MPs voted with the Tories.
The vote reduced Labour's 67-strong majority by more than two-thirds and will be a warning shot to Gordon Brown.
Shadow business secretary Alan Duncan said the result was "astonishing" and proved his party had won the argument.
Business Minister Pat McFadden said the programme was vital because of fewer customers and heavy losses - but he would consider plans by some councils to take over branches under threat.
A government amendment commending its actions in subsidising the network was backed by 290 to 251, a majority of 39.
Rebel MP John McDonnell said: "The government has always underestimated the strength of anger on Labour benches against the privatisation and cuts in this essential public service.
"Tonight's vote is a huge embarrassment to the government and shows that a large number of Labour MPs are even prepared to support a Tory motion to demonstrate their concern.
"The government is the sole shareholder in Royal Mail and could stop this closure programme in its tracks."
Some 19 Labour MPs voted for the Tory motion, along with Robert Wareing, who quit the party last year after failing to be reselected to fight his seat and now sits as an independent.
Tory leader David Cameron did not take part in the vote. A Conservative Party spokesman said he had been forced to return home to look after his children.
Shadow business secretary Alan Duncan urged Labour MPs to rebel, arguing that 90 of them, including seven in the Cabinet, had been campaigning against the post office closures.
Mr Brown had told MPs he wanted to see good Post Office services in every part of the country but argued that the organisation was losing £500,000 a day.
He said the Tory measure had not promised extra cash for the Post Office, adding: "Unfunded promises are empty and hollow promises to the people of this country."
But after the vote, Mr Duncan said: "The government has just squeaked home; it's astonishing that it was only a majority of 20. The power of argument has overcome the power of their whips.
"The hunt will now be on for all those Labour MPs who have pretended to support their local Post Office and then done a runner when they had a chance to make a real difference."
He said the closure programme was being "rammed" through and "community is being pitted against community" in an attempt to keep their branch.
While the Tories fully expected the network to "shrink in size", they had never given a guarantee that there will be no post office closures, he said.
Mr Duncan said the six-week consultation on which post offices are to close "is a sham".
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But Mr Hutton claimed the Tory motion to suspend the closures was based on "false hopes, flawed economics and opportunism".
There was an "inescapable fact" that had to be accepted, "however difficult" - the role of the Post Office has changed because of technology and consumer behaviour - he said.
"These have both combined to reduce very substantially the numbers of people using their local sub-post offices and increased substantially the losses being incurred by the Post Office."
However, Mr Hutton said he wanted the Post Office to give "serious consideration" to a proposal by Essex County Council, to take over and run post offices earmarked for closure in the county.
Sarah Teather, the Lib Dem business spokeswoman, said: "These closures rip the heart out of the centre of the community."
Tory Tim Loughton accused the Post Office of "sticking two fingers up at pensioners, at local business, the community at which the Post Office forms the heart... and they have the temerity to call themselves the 'People's Post Office'".
Labour's Martin Salter said the consultation had been "less than transparent and at times shambolic".
When the programme for post office closures was announced in 2006, ministers pointed out that the government had invested £2bn in the network since 1997 and would commit an extra £1.7bn until 2011.