They agreed to a government proposal to extend Stormont's talks until 29 June.
During the debate, the secretary of state also confirmed plans to provide legal authority for a Stormont budget, if the parties cannot reach a deal.
Stormont has been without a devolved government since January, when a coalition led by the DUP and Sinn FÃ©in fell apart over heating scheme scandal.
The Ministerial Appointments and Regional Rates Bill gives the parties more time to negotiate after the general election on 8 June.
It also allows rates to be collected in the absence of a devolved government.
It took just under four hours for MPs to discuss the legislation proposed by Northern Ireland Secretary of State James Brokenshire.
He argued that his bill provides the scope and space for the local parties to strike a political deal.
But proof that the government is planning for failure as well as success came in his confirmation that he has been talking to senior civil servants about the budget for the current financial year.
If implemented, Mr Brokenshire's indicative budget position will provide certainty, but a projected 2.5% cut to the education budget will undoubtedly cause concern.
The debate in the House of Commons was wide-ranging, touching on issues like the Irish language, same-sex marriage, the military covenant and Brexit.
The House of Lords will debate the bill on Wednesday and then the legislation, which is being fast-tracked through Parliament, should become law by the end of this week.

Analysts said June's hot weather had helped to lift sales at the company, which also includes Argos.
The UK's second biggest supermarket said like-for-like sales - which strip out the impact of new stores - grew by 2.3%, excluding petrol.
Chief executive Mike Coupe said he was "pleased" with the results - its best growth in four years.
Laith Khalaf, an analyst at Hargreaves Lansdown, said: "The recent heatwave helped to boost sales at Sainsbury's group, as customers turned to the Argos website to buy electric fans and paddling pools to keep cool in the hot weather."
Demand for deals on British strawberries and its summer eating range added to Sainsbury's grocery sales, which were up 3%.
Food price inflation also contributed to a rise in sales at the supermarket's checkouts.
This is the best quarterly performance by Sainsbury's in years, with sales up across the board. Like the other main supermarkets, inflation is driving some of this sales growth.
The boss said the company had managed to "keep a control over prices" and that the rise in own label goods had been a big success.
Was this a sign of shoppers trading down, for instance eating in instead of eating out? Chief executive Mike Coupe said there wasn't any evidence of a massive change in consumer behaviour although there might be a trend starting to come through.
Most striking though is the rise in clothing sales - up by more than 7%, a very strong performance, in stark contrast to its competitors on the high street. A sign, perhaps, that consumers are watching their wallets.
Mr Coupe said "inflation was coming through", but that Sainsbury's was trying to keep prices down by striking deals with suppliers.
He pointed to chicken, milk and broccoli, which he said were cheaper than three years ago.
The company's latest sales figures marked an acceleration from the previous quarter when sales grew by just 0.3%.
The growth was also slightly stronger than expected, with analysts having forecast like-for-like sales to grow 2%.
David Alexander of GlobalData, said: "Even accounting for a later Easter and Mother's Day, and the inclusion of a buoyant Argos in the figures, the numbers still present a positive picture."
Widespread media reports have suggested Sainsbury's is lining up Nisa, a convenience store chain and wholesaler, for its next acquisition.
George MacDonald, editor of Retail Week, told the BBC that Sainsbury's was "possibly grabbing on the coat-tails of Tesco which wants to buy another wholesaler called Booker".
However, Mr Coupe declined to comment on any possible Nisa deal, saying it regularly looked at potential tie-ups.
"We are not holding onto anyone's coat-tails - that's just the nature of a large corporation. Most of these conversations come to nothing," the Sainsbury's boss told reporters.
MPs have passed a bill delaying the deadline for Northern Ireland parties to reach a deal to restore devolution.
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Sainsbury's has said sales of clothes, summer food and paddling pools helped speed up growth in the past few months.