MPs voted by 329 to 302 to back an amendment which will allow the House of Commons to stage a series of "indicative votes" later this week which are designed to guide the government's next steps on Brexit.
The result means the House of Commons will on Wednesday have the power to vote on alternatives to May's plan which are expected to include a softer Brexit, a second referendum, and potentially revoking Article 50.
The Business Minister Richard Harrington resigned from the government in order to back the amendment.
In his resignation letter, Harrington accused May's government of "playing roulette with the lives and livelihoods of the vast majority of people in this country".
May had previously considered plans to bring forward her own version of indicative votes, but resisted confirming such a vote on Monday, saying she remained "sceptical" of such votes.
"I continue to believe doing so would be an unwelcome precedent to set which would overturn the balance of our democratic institutions," she said.
"I must confess that I am sceptical about such a process of indicative votes. When we've tried this kind of thing in the past, it's produced contradictory outcomes or no outcome at all."
The amendment, which was brought forward by Conservative MP Oliver Letwin, was passed despite attempts by ministers to persuade MPs that "time would be made available" to hold some form of indicative votes at some point in the future.
It also came after the prime minister abandoned her plans to hold a third "meaningful vote" on her Brexit deal this Tuesday.
The prime minister told the House of Commons on Monday afternoon that she had abandoned her plans to hold a vote as "there is still not sufficient support in the House to bring back the deal."