Face of Nation : The House of Commons supported both measures via amendments to legislation designed to keep Northern Ireland running in the absence of a devolved executive.
The amendments were passed overwhelmingly after MPs were given free votes on Tuesday afternoon.
Same-sex marriage and abortion are traditionally treated as a matter of conscience in the Commons.
Legislation to allow same-sex marriage in England, Wales and Scotland was passed in 2014 but has never been introduced in Northern Ireland.
Meanwhile, abortion is presently illegal in Northern Ireland in all but the most extreme circumstances.
There has been no devolved government in Northern Ireland since January 2017, following the collapse of a power-sharing deal between the DUP and Sinn Fein.
Despite the recent resumption of talks between the Northern Irish parties, they have yet to reach a new agreement.
It meant the UK government was forced to bring forward the Northern Ireland (Executive Formation) Bill to extend the period of time for the formation of a new Stormont administration.
Labour MP Conor McGinn’s amendment to the bill adding the provision on same-sex marriage was supported by 383 votes to 73, a majority of 310.
His fellow Labour MP Stella Creasy’s amendment adding the provision on extending abortion access was supported by 332 votes to 99, a majority of 233.
Ms Creasy posted on Twitter after the votes: “Thank you to everyone who today stood up for equality in Northern Ireland – whether for same sex marriage or abortion, today we have said everyone in the UK deserves to be treated as an equal.
“There’s a road to go yet but today a big step forward.”
Labour’s shadow Northern Ireland secretary Tony Lloyd said: “Today parliament has voted to ensure that love no longer has borders and women are not treated as second-class citizens.
“The government must now act to bring forward legislation on marriage equality and abortion reform if the Northern Ireland Assembly and executive are not returned before 21 October.
“Labour has long called on the government to take action on these issues and will work with the government to see it implemented.”
A large number of SNP MPs added their support to both the amendments despite usually abstaining on devolved issues.
The party’s leader and Scottish First Minister Nicola Sturgeon posted on Twitter: “Would rather the Northern Ireland Assembly was doing this but in its absence, marriage equality and human rights can’t wait.
“This is the right decision in the circumstances.”
