Only hours before the vote, Mrs May had told Cabinet that "candid" legal advice given to ministers must remain confidential, despite a Commons vote last month demanding its publication in "final and full" form.
A binding Commons vote in November, however, required the government to publish "any legal advice in full".
May wants to secure parliament's approval for her deal to keep close ties with the European Union after leaving in March, but opposition is fierce, with Brexit supporters and opponents alike wanting to thwart or derail her plan.
The vote has little direct impact on the Brexit debate, but reflects mounting tension between the government and Parliament over the next steps in Brexit.
Scottish MPs and MEPs had brought the case on Article 50 - a 250-word clause inserted into the EU charter eight years ago, which had never been used until the United Kingdom voted to exit the European Union in the summer of 2016.
Starting Tuesday, the British Parliament will debate whether to accept the terms of the deal that was negotiated by May and representatives from the European Union.
"Don't imagine that if we vote this down another deal is going to miraculously appear", Mrs May insisted.
The governing Conservative Party and the main opposition party, Labour, are internally divided on how Brexit should proceed.
"But the reality remains that we have an unsatisfactory procedure to resolve differences of opinion in this House, if and obviously, it's an if, we come to a point where the Government does not succeed on its motion and the opportunity exists this afternoon to cure that anomaly".
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Labour's Brexit spokesman Keir Starmer said: "This House has now spoken and it's of huge constitutional and political significance".
But that was not true, given the House of Commons vote, the advocate general said.
In practice, it means that should Parliament refuse to accept the prime minister's deal, MPs could instruct her to extend negotiations, hold another referendum, or pursue a different sort of Brexit like a softer, Norway-style exit.
"I'm focusing on ... getting that vote and getting the vote over the line", she said.
In an opinion issued before a judgement by the European Court of Justice, Advocate General Manuel Campos Sanchez-Bordona rejected the contention that Article 50 can only be revoked following a unanimous decision of the European Council, made up of the EU's member states.
Mr Maugham added: "On this critical issue I'm sure MPs will now search their consciences and act in the best interests of the country".
"We should not let the search for a ideal Brexit prevent a good Brexit which delivers on the wishes of the British people".
In the most extreme no-deal scenario, shopping bills could rise by up to 10% but even in an orderly no-deal withdrawal, with a transition period, grocery prices could rise by 6%, he said.
The Conservative leader was set to tell MPs in a speech later on Tuesday that the deal "delivers for the British people".