MPs have approved Conservative MP Sir Graham Brady's Brexit amendment, which aims to replace the Northern Ireland backstop with "alternative arrangements".
The Government-backed motion was voted through by 317 votes to 301 – a majority of 16.
The amendment was one of two out of the seven motions to be passed, with the other being Conservative’s Dame Caroline Spelman's amendment.
Dame Spelman’s amendment seeks to prevent the UK from leaving the European Union without a deal, and was approved by 318 votes to 310 – a majority of only eight.
All other amendments, including one by Labour MP Yvette Cooper calling for Parliament to gain control over the Brexit process if Theresa May failed to secure a deal by February 26, were voted down.
The amendment, which could have given MPs the power to prevent no-deal Brexit or extend Article 50, was defeated by 321 votes to 298 – with a majority of 23 against it.
The largest defeat was on SNP’s Westminster leader Ian Blackford’s amendment, which only had 39 votes in favour.
'I look forward to meeting the Prime Minister'
Watch: Labour leader Jeremy Corbyn agreeing to meet the Prime Minister.
Mrs May secured the backing of the Commons to go back to Brussels, as MPs voted in favour of the proposal from Mr Brady for her to try to replace the backstop with "alternative arrangements" to keep the Irish border open after Brexit.
Speaking after the votes, the Prime Minister said: "Tonight a majority of members have said they would support a deal with changes to the backstop combined with measures to address concerns over Parliament's role in the negotiation of the future relationship and commitments on workers' rights in law where need be.
"It's now clear there is a route that can secure a substantial and sustainable majority in this House for leaving the EU with a deal.
"We will now take this mandate forward and seek to obtain legally binding changes to the Withdrawal Agreement that deal with concerns on the backstop while guaranteeing no return to a hard border between Northern Ireland and Ireland."
Labour leader Jeremy Corbyn also agreed to meet Mrs May after Dame Spelman's amendment against no-deal Brexit was approved.
"Since we have had this debate and the House has emphatically rejected the no-deal option, could I say that we are prepared to meet her to put forward the points of view of Labour Party of the kind of agreement we want," he said.
"To protect jobs, to protect living standards and protect rights and conditions in this country. It is exactly the offer that was made in September, exactly the offer made two weeks ago and I look forward to meeting the Prime Minister to set out those views to her on behalf of the party.”