Ministers have conceded there are lessons to be learnt from Tuesday's five-vote victory on tuition fees.
Blair faces continued opposition over top-up fees
They accepted mistakes were made in the way the idea for variable fees was introduced, after 72 Labour MPs voted against the government.
Some rebel MPs pledged to fight on as the bill goes through Parliament.
Ex-Labour Cabinet minister Jack Cunningham compared the Labour splits with the party's fight against the militant tendency during the 1980s.
The Higher Education Bill was backed by 316 votes to 311, after days of intense campaigning by both sides.
Mr Blair had staked his authority on winning the vote, which saw a sharp reduction in his usual 161 majority.
It was widely seen as his biggest test as prime minister and came just hours before Lord Hutton was due to report his findings on events surrounding the death of weapons expert Dr David Kelly.
It means the bill has passed its first major hurdle, but the plans will still be put to the test in further votes in the Commons and Lords as it goes through the parliamentary process.
MPs are now likely to spend two to three months going through the bill line-by-line in its committee stage.
Even staunch Blairites like former health secretary Alan Milburn said that in future such important reforms should be debated before being launched on an unsuspecting public, BBC political correspondent John Andrew said.
Before the vote deputy prime minister John Prescott told BBC News 24: "I don't think it's been handled very well - a 160-odd majority and scrambling around to get a few to come into the vote."
Many see the hand of the chancellor, Gordon Brown, in delivering Tony Blair's victory.
The sudden decision by his close ally and rebel leader Nick Brown to back the bill may have been crucial.
But its thought only a handful of MPs were persuaded by his sudden decision to switch sides.
Ex-Labour Cabinet minister Jack Cunningham told BBC Radio 4's Today it was not just Mr Blair who needed to learn from "bitter divisions" within the party.
He warned members of the parliamentary Labour party they were "not elected to bring down its own government".
Asked on the BBC's Today programme if he was really likening them to Militant, he said: "A former chief whip, a former deputy chief whip openly, coherently working and planning to bring defeat to their own government? It gets perilously close to that doesn't it?"
One of the bill's opponents, Norwich North MP Dr Ian Gibson, said: "I will never sleep until I get rid of variable fees."
Speaking for students, Mandy Telford said the NUS refused to "believe that MPs have been won over by concessions".
"This fight is not over - we will take it to committee stage, to amendments and to the Lords."
After the result Education Secretary Charles Clarke told BBC News: "Had we lost it, it would have been a blow to our authority but as it is we have the ability to take the legislation forward."
The minister said divisions always caused "a bit of damage" but were not surprising over such serious reforms.
Both the Conservatives and Liberal Democrats opposed the plans, which would allow universities to charge students £3,000-a-year, payable when they earn £15,000.
Shadow education and health secretary Tim Yeo branded the result an "utter humiliation" for ministers.
"The government had only won because Scottish Labour MPs voted to impose fees on English students which would not apply north of the border," he said.
Ex-Tory leader William Hague urged the government to "consign this bill to the rubbish heap".
Liberal Democrat leader Charles Kennedy said: "Nobody has emerged from this shabby compromise with any credit."