Labour's motion sought to compel the Government to provide to the Exiting the European Union Committee the 58 studies showing the potential impact of Brexit on different industrial sectors.
The Government earlier stood firm on its stance of not releasing the full Brexit impact assessments.
But Brexit minister Robin Walker, while confirming the Government would not oppose the motion, said he had taken note of Labour's points about looking at "redaction or summary as approaches".
Tory Jacob Rees-Mogg (North East Somerset) told the debate: "I have no doubt this motion is, in all senses, binding.
PAPrime Minister Theresa May in Parliament
"It is not parliamentary wallpaper. It's exercising one of our most ancient rights - to demand papers."
He said he would have supported the Government if it had opposed the motion, adding: "In the event it does not, it must publish these papers to the Brexit select committee in full.
"This motion does not allow a redaction and a happy chat across the despatch box between the shadow spokesman and the ministers does not reduce the right of this House to see the papers."
Liberal Democrat Brexit spokesman Tom Brake said: "The government has been keeping people in the dark for too long about the impact of their extreme Brexit plans.
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"Parliament has now made its position clear.
"Ministers need to publish these reports in full, not subject them to a Whitehall whitewash.
“This has nothing do with Britain’s negotiating position, and everything to do with the government trying to spare its own blushes.”Related articles
PAShadow Brexit Secretary Keir Starmer
Labour’s Shadow Brexit Secretary said: "This is a victory for Parliament and for democracy.
“Labour has been absolutely