The UK is now due to leave the European Union on March 29, but Thursday evening's 412-202 vote in Parliament would push Brexit back to at least June 30, providing that the rest of the 27 European Union countries agree to the delay.
A delay would also see Britain take part in European Parliament elections in May - bizarrely re-immersing the country in EU politics after Brexit was originally meant to have gone into effect. Today Chancellor Philip Hammond hinted that Attorney General Geoffrey Cox could revisit his legal advice on whether Britain would be trapped in the Irish backstop "indefinitely" - unlocking votes for Mrs May's deal.
Britain is scheduled to leave the European Union on March 29 - with an agreement, if it's approved, or without a deal.
Theresa May could simply put her deal to a vote again.
So after more than two and half years steeped in stalemates, Parliament finally agreed on something: additional time to debate the same deal it's already twice rejected, while giving concerned businesses and an exhausted public no new assurances on how this will end. That's expected to happen though, since the European Union fears the United Kingdom crashing out of the bloc in a chaotic no-deal Brexit-still the default, by the way-perhaps as much as the United Kingdom itself.
And by the far narrower margin of 314-312, they voted down a cross-party bid for parliament to seize control of the Brexit process.
The motion also supported holding a third vote early next week on May's twice-rejected deal.
The vote in Parliament was on whether to seek a delay of at least three months to Brexit, which now is due to take place March 29.
First up is that hugely controversial and fascinating vote on whether to back a second referendum.
Conservative MPs were given a free vote on the government's motion on Thursday, reflecting deep divisions over the best way forward, with just a fortnight to go before the planned exit day.
The DUP has welcomed the government's "renewed focus" on addressing its objections to the Brexit deal ahead of next week's third Commons vote.
May has refused to abandon her unpopular deal, and is seeking to win over opponents in her own party and its Northern Irish political ally, the Democratic Unionist Party.
Still, she faces a struggle to overturn the huge defeats for the agreement, which was rejected by 230 votes in Parliament in January and by 149 votes this week.
Charles Walker, a senior Tory backbencher, has said May will have to hold one.
If the delay is approved next week, May hopes to use it to enact legislation needed for Britain's departure.
She is proposing that Brexit be delayed until June 30 - but only if she Parliament approves her Brexit deal.
The European Commission recalled Thursday evening that "any request for extension of (the period of negotiations provided for by) Article 50 requires the unanimous agreement of the 27 other member countries" and should be duly justified.
Dodds also denied that additional funds for Northern Ireland were being talked about as an incentive for the DUP to vote for the deal: "We're not discussing cash in these discussions, this is about Brexit".
"Under no circumstances an extension in the dark!" tweeted the European Parliament's Brexit coordinator, Guy Verhofstadt.