An earlier version of the plan was defeated by the largest margin in parliamentary history.
Two of Wales' eight Tory MPs voted against the deal - Guto Bebb and David Jones - while the rest backed it.
Mrs May said the votes today showed there was a clear majority against no-deal deal.
Stamford MP slams 'control freak' PM as he seeks to remove 'No Deal' Brexit
Deal or no deal?
The lawmaker proposing each amendment can choose not to put it to a vote.
European officials expressed irritation and skepticism on Wednesday over the Brexit standoff in the British parliament, which rejected for a second time a deal negotiated by Prime Minister Theresa May with the EU.
The humiliating defeat came approximately two months after the same deal was rejected by a majority of 230 MPs, giving May one of the worst defeats for a sitting government in British history.
There were 391 votes against the deal, but this time all of our MPs supported the PM.
Kier reveals higher debts in revised statement
Shares in Kier Group crashed on Monday as the construction company revised up its net debt position. The company's FY19 interim results will be released on 20 March 2019.
Juncker said he recommended the deal to the EU Council, which represents member states, and that Irish Prime Minister Leo Varadkar was prepared to back the changes on the backstop. Hard-core Brexit supporters in May's Conservative Party and the prime minister's allies in Northern Ireland's Democratic Unionist Party both said they could not support the deal.
British Prime Minister Theresa May's amended Brexit solution has crashed in Parliament, ensuring even more chaos before this month's do-or-die deadline.
"No deal must be taken off the table".
But if there is a no-deal Brexit, things are a lot more uncertain - the Government has been ramping up preparations to try to prevent shortages of food and medicine amid fears that increased bureaucracy will clog up key ports where goods arrive from the Continent.
Boris Johnson, the former Foreign Secretary who quit over Mrs May's tactics, said the premier's plan had "reached the end of the road".
California governor puts moratorium on executions
His order also points to the 164 people who have been freed from death row after they were found to be wrongfully convicted. Newsom's moratorium will therefore fly in the face of the most recent expression of the views of the people of California.
MPs will be called to cast another vote tomorrow on delaying Brexit.
To many lawmakers who had voted down May's deal for the first time in January because of concerns over the "backstop", Cox's advice provided evidence that their concerns had not been sufficiently met. While some tweaks were made, Juncker did not agree fully to May's central change, firm guarantees on the Ireland backstop - the main issue at the heart of lawmakers' disapproval. Why would European Union leaders engage with her again after yet another failure?
But following the surprise result on the amendment by Caroline Spelman, European Research Group chairman Jacob Rees-Mogg said the amendment had no legal force.
Sterling had steadily risen on foreign currency exchanges throughout the day amid speculation that a no-deal Brexit was becoming less likely, before rising more sharply in the evening. "The government's strategy is now in tatters".
"It is harder to leave the backstop than it is to leave the European Union", claimed Conservative MP Jacob Rees-Mogg, an influential Brexiteer.
Christopher Nolan’s ‘Dark Knight’ Trilogy Returns to IMAX Theaters in Limited Release
Portions of The Dark Knight specifically used special IMAX equipment to get the full scope of the Hong Kong action sequences. Each of these screenings will be accompanied by footage of Christopher Nolan's aforementioned Q&A session.
"I don't say it's going to happen, but clearly if a government can't get through on the one issue which we were really elected to deal with at the last election it puts us all in a very hard situation".