In the teeth of fierce backbench opposition, MPs voted to give the Education and Inspections Bill a second reading by 458 votes to 115, with 51 Labour rebels joining Liberal Democrats in the "no" lobby.
With 51 Labour rebels, the Prime Minister's relief will be shortlived as he only won the vote because of Conservative backing.
More than 90 Labour backbenchers were initially opposed to the reforms aimed at creating "trust" schools with greater freedom and independence.
But concessions on admissions policy, selection and the role of local authorities in building new schools won back many rebels.
The Welsh Assembly government has opted out of the "trust" proposals, but is adopting sections of the Bill covering pupil behaviour, discipline and exclusion, and food and drink in schools.
It is also seeking powers to develop policy in areas including school admissions, re-organisations, and the 14-19 curriculum.