Rebel Tory MPs and the DUP – who 24 hours earlier rejected the PM’s Brexit plan by a huge margin – voted to keep her in Downing Street.
Labour leader Jeremy Corbyn argued that Mrs. May’s “zombie” administration had lost the right to govern.
Mrs. May will be making a statement from Downing Street at around 2200 GMT.
The PM won the vote by a margin of 19, including 10 votes from the DUP. Had the party voted against her, she would have lost by one.
Giving her reaction to the result, Mrs. May told MPs she would “continue to work to deliver on the solemn promise to the people of this country to deliver on the result of the referendum and leave the European Union”.
She invited leaders of all parties to have individual meetings with her on the way ahead for Brexit – starting tonight with offers made to the Westminster leaders of Labour, the Liberal Democrats, the SNP, and Plaid Cymru – but called on them to approach them with a “constructive spirit”.
“We must find solutions that are negotiable and command sufficient support in this House,” she added.
But Mr. Corbyn, who tabled the no-confidence motion, said in the Commons that before any “positive discussions” could take place, the prime minister should rule out a no-deal Brexit.
“The government must remove clearly, once and for all, the prospect of the catastrophe of a no-deal exit from the EU and all the chaos that would come as a result of that,” he told MPs.
His spokesman later said that Downing Street had spoken to the Labour leader’s office before the vote about a prospective meeting, but that he was not expected to go to No 10 this evening.
Mr. Corbyn’s no-confidence motion was backed by all the opposition parties, including the Scottish National Party and the Liberal Democrats.
His party has not ruled out tabling further any confidence motions – but Mr. Corbyn is under pressure from dozens of his own MPs and other opposition parties to now get behind calls for a further EU referendum instead.
The leader of the SNP in Westminster, Ian Blackford, met Mrs. May following the vote to discuss a way forward with Brexit.
After the meeting, he wrote to the PM and called for a “clear gesture of good faith” from her, by confirming that the extension of Article 50, a ruling out of a no-deal Brexit and the option of a second EU referendum would form the basis of future discussions.
Mr. Blackford has also written to Mr Corbyn, along with other opposition leaders, to urge him to back another referendum as Labour’s official position.
He added: “We must see concessions from the prime minister, as well as Jeremy Corbyn, to break the Brexit impasse.”
The leader of the Liberal Democrats, Vince Cable said it would be “silly not to talk” to the government, but agreed with Mr Blackford that no deal had to be taken off the table, as well as the PM having a “willingness” to discuss another referendum – which is the party’s preference.
Sir Vince also reiterated his calls for Mr. Corbyn to get behind the “People’s Vote” too now that he had lost his no-confidence motion.