The Education and Adoption Bill addresses the problem of underperforming "coasting" schools, but allows less challenge or consultation.
Labour peers wanted more consultation for parents and said academy status was not the only way to improve schools.
"It seems no opposition is to be tolerated," said Labour's Lord Watson.
But the government survived an opposition amendment when the result was tied at 219 votes on both sides, another amendment was defeated by a margin of 14 votes.
Education Minister Lord Nash said the government's plans were manifesto commitments and weak schools needed urgent improvements without excessive procedural delays.
Last week, Education Secretary Nicky Morgan introduced her own amendment to the plans so that failing academies would also come under scrutiny, with the expectation that they would be taken over by another academy chain.
Prime Minister David Cameron has said that local authorities running schools should become a "thing of the past".
Shadow education minister Lord Watson said there was no evidence to show academies were inherently better than local authority schools.
And he warned an excess of "political dogma" was behind the push for academies and excluding the views of parents would create "mistrust and resentment".
Baroness Pinnock, from the Liberal Democrats, said the government should not "dictate" to parents about changes to their local schools.
But Conservative peer Lord True questioned why the process of improving schools should be held up by those who had previously been responsible when schools were struggling.
Lord Harris, Conservative peer and academy sponsor, said that too often there had been delays in tackling failing schools - and that much progress could be achieved quickly if the government allowed academy chains to intervene.
Ahead of the debate, Mrs Morgan had written that peers had to choose between "improving the life chances of children neglected for decades and giving in to the vested interests that oppose reform".
The education secretary said the plans would ensure "all children receive the standard of education they deserve" - and the opposition amendments would preserve "the loopholes exploited by campaigners" against academies.
After the opposition amendments were defeated, a Department for Education spokesman said: "We are pleased the Lords have decided to put the interests of children ahead of all others in tonight's votes on the Education and Adoption Bill.
"The bill is central to our commitment to delivering educational excellence in every part of the country.
"It seeks to improve the life chances of every child by giving our best school leaders the freedom to transform failing schools and introducing new measures to allow us to properly tackle coasting schools."
But an alliance of education organisations, including the National Governors' Association, the Catholic Education Service and teachers and head teachers' unions, said they were "disappointed" by the outcome.
"The government is wrong is wrong to say there is only one pathway to school improvement.  Becoming an academy does not guarantee the higher standards of education for children that they say it does," says a statement from the education group.
"The government is wrong to portray the many voices of parents and experts as 'vested interests'. The process of academy conversion is also too opaque for people to be confident that it will be fair.
"The evidence clearly shows that there is no link between academy status and automatic school improvement, so it is right that concerns are raised, and not dismissed simply because they conflict with the government's desire. Children should not have their futures put at risk by such a flimsy set of proposals."
The government has survived a challenge in the House of Lords to its plan to fast-track more local authority schools in England to become academies.