The Commons backed the move on equal marriage by 383 votes to 73, majority 310, and on abortion by 332 votes to 99, majority 233, after Theresa May and Jeremy Corbyn gave Tory and Labour MPs a free vote, as the issues are a matter of conscience.
Labour’s Conor McGinn’s successful amendment to the Northern Ireland (executive formation) bill requires Westminster to legalise same-sex marriage.
Stella Creasy, Labour MP for Walthamstow, meanwhile led efforts to extend access to abortion by requiring Northern Ireland Secretary Karen Bradley to make regulations to give effect to recommendations from a report.
Both would come into effect by October 21 unless a new Stormont executive is formed before this date.
McGinn said MPs had been failing LGBT people in Northern Ireland by not acting previously.
But he made clear his proposals were an interim provision in case the assembly, which collapsed in acrimony between power-sharing parties in January 2017, failed to reconvene.
The St Helens North MP said: “This House has failed LGBT people in Northern Ireland before.
“It failed a generation of people in Northern Ireland by not decriminalising homosexuality and condemn them to discrimination, to abuse and to living in fear many years after that stopped to be the case in the rest of the UK.
“It failed people in Northern Ireland by not extending same-sex marriage when it became the law here making people in Northern Ireland less valued than the rest of us.”
Talks are ongoing to restore the power-sharing assembly and executive, and McGinn conceded that Northern Ireland could overturn MPs’ decision if they reconvene, as the issue is a devolved matter.
But he insisted: “At the minute the executive and the assembly exists in the ether or as a concept, not a reality.
“So if they can’t make this law, we will make it here because - as I have said often - rights delayed are rights denied.
“We will make the law here and then when the assembly is back up and running the power remains for them to change it.”
Shadow Northern Ireland minister Karin Smyth said voting to pave the way for equal marriage in Northern Ireland would be a “great testament” to murdered journalist Lyra McKee.
Speaking about Ms McKee’s funeral, Ms Smyth told MPs: “We heard that day was that Lyra was making arrangements for her own marriage to her partner.
“It really struck me sitting in the cathedral of the huge sadness, the huge irony, when we rightly praised this remarkable young woman for being a child of the peace process, for being so openly happy with her own sexuality, with having touched every part of Northern Ireland society with her optimism.
“That she was making those plans for her own marriage to the woman that she loved but what her own society was saying to her was essentially ‘away you go to Donegal, you can’t do that here’.
“What a great testament it would be to her memory and the thousands of people across Northern Ireland who simply want to express their love that we would make progress on this issue.”
Creasy said the United Nations torture committee has “censured” the UK over abortion rules in Northern Ireland, saying the way women are treated is “torturous”.
She added: “At this moment in time, if somebody is raped in Northern Ireland and they become pregnant and they seek a termination, they will face a longer prison sentence than their attacker.”
Critics however voiced concerns that Westminster imposing laws on Northern Ireland could harm the devolution settlement and talks aimed at restoring power-sharing.
DUP Westminster leader Nigel Dodds said the amendment was “seeking to drive a coach and horses through the principle of devolution, overriding the concerns of people in Northern Ireland”.
Independent unionist MP Lady Sylvia Hermon said her constituents were concerned about the damage this vote could have on the devolution settlement.
The North Down MP added: “They are greatly concerned that this amendment might undermine the devolved settlement in Northern Ireland.”
Simon Hoare, Conservative chairman of the Northern Ireland select committee, said he was “very frightened” these amendments could collapse the talks to re-establish power-sharing at Stormont.
Hoare said: “If they proved to be a reason, an excuse or smokescreen to collapse the talks coming from either end of the spectrum, that would be lamentable.
“I do not believe that this House should do anything to jeopardise those fragile talks.”