A majority of 41 approved an amendment that blocks suspension between 9 October and 18 December unless a Northern Ireland executive is formed.
MPs are now voting on a Lords amendment which proposes a similar measure.
Tory leadership frontrunner Boris Johnson has not ruled out suspending Parliament.
BBC political editor Laura Kuenssberg said the Commons had now made it harder for a new prime minister to suspend Parliament.
Amendment passed comfortably… 315 to 274 – majority of 41 with lots of abstentions – Commons just made it harder, altho not impossible for hypothetical Johnson PM to suspend parliament
— Laura Kuenssberg (@bbclaurak) July 18, 2019
Mr Johnson’s rival Jeremy Hunt has ruled out suspending Parliament.
If the 31 October deadline is reached without Parliament backing an agreement between the UK government and the EU, the UK is scheduled to leave the EU without a deal.
MPs have consistently voted against a no-deal Brexit, but the prime minister could try to get around that by suspending Parliament – proroguing – in the run-up to the deadline, denying them an opportunity to block it.
But the House of Lords’ amendment to the Northern Ireland (Executive Formation) Bill would require progress reports on restoring devolved government in Northern Ireland to be debated regularly in Parliament, effectively preventing it being shut down.
It builds on an amendment from pro-EU Tory Dominic Grieve passed by MPs last week that would require ministers to give fortnightly reports to Parliament throughout October on progress to restore devolution.
The new Lords amendment would ensure these have to be debated in the weeks before the Brexit deadline – meaning MPs and peers have to sit.
But this tweak will have to be approved by MPs in order to make it into the final version of the bill.
Former Foreign Office minister Alistair Burt, who is supporting a further amendment to explicitly block suspension of Parliament, along with Brexit committee chairman and Labour MP Hilary Benn, said this change would further strengthen the measures against the suspension of Parliament.
He said it was “in order to make sure that we reflect the views of our constituents by being here (in Parliament)”.
Former education secretary Justine Greening told MPs: “What have we come to in Britain when we have to amendments to ensure Parliament can still operate?
“Firstly you don’t win a debate by closing down the main chamber in which the country’s people’s views are aired and you don’t unite a country by muzzling the representatives of people around those communities.”
She said if Parliament were to be suspended, “this House would not be there to debate other issues that might arise during that time”.
She said it was “entirely untenable” and “actually quite dangerous to shutdown Parliament as a time of such uncertainty”.
But DUP Westminster leader Nigel Dodds said it was “very disconcerting” to see a bill about Northern Ireland “hijacked for other purposes and particularly to see the debates taking place not even on the issues that directly affect Northern Ireland”, like marriage and abortion.
And Northern Ireland Minister John Penrose said the amendments attempting to block no deal were “pretending to be democratic but trying to prevent the democratic referendum decision from ever happening at all”.
Earlier, Justice Secretary David Gauke, an opponent of a no-deal Brexit, told BBC Radio 4’s Today programme that proroguing Parliament would be “outrageous”, but did not confirm whether he would back measures to block it.
Pressed on whether he would resign from the government to vote in favour of the change to the Northern Ireland Bill, he replied: “I’ve said what I’ve said and you can interpret that as you wish.”
Former Tory prime minister John Major has said he will seek a judicial review if the next prime minister tries to suspend Parliament.
Campaigner Gina Miller has threatened the same action.
At Conservative Party leadership hustings, when asked about suspending Parliament, Mr Johnson said he would “not take anything off the table”.
He said he wanted to leave the EU on 31 October “come what may”.
Downing Street said forcing a report and debate every two weeks “risks being counter-productive” to the aim of restoring the executive in Northern Ireland.
The prime minister’s official spokesman told a Westminster briefing: “We have been very clear that the purpose of this bill is to ensure the continuation of vital public services and effective governance for the people of Northern Ireland.”