After a three-hour debate, the House of Lords voted 366 to 268 to back calls for a "meaningful vote" on the final terms of withdrawal from the 28-member bloc.
Peers yesterday amended the legislation that will authorise May to notify the EU of the UK's intention to leave and pave the way for official Brexit talks to begin.
It is the second defeat the Lords has inflicted on Prime Minister May over the Brexit bill, giving her the power to trigger Article 50 talks, after she and her ministers demanded it be passed by Lords unamended.
The Brexit secretary David Davis said the government would try to throw out the amendment and a previous one that would guarantee the rights of EU citizens in the UK when the Brexit bill returns to the House of Commons on Monday.
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"It is disappointing that the House of Lords has chosen to make further changes to a bill that the Commons passed without amendment," he said.
"It is clear that some in the Lords would seek to frustrate that process, and it is the government's intention to ensure that does not happen. We will now aim to overturn these amendments in the House of Commons," Davis said.
The latest defeat has dashed Prime Minister May's hopes, who was confident of passage of the bill in time to meet her deadline of triggering Article 50 of the EU's Lisbon Treaty, which begins the two-year withdrawal process, by the end of the month.
May's Conservative Party has a majority in the lower chamber, but not the Lords, the upper chamber.
This back-and-forth threatens the Article 50 deadline.
May has previously agreed to give the parliament a vote on her Brexit deal, but on a "take-it-or-leave-it" basis. That means if lawmakers dismiss May's divorce agreement with EU, the UK could be out of the trading bloc without any deal in place.