The Home Office refused travel visas for the pair over concerns they weren't wealthy enough and may try to seek asylum here.
They had planned to visit Scotland as part of a twinning link between the Church of Scotland's Glasgow Presbytery and the Diocese of Hyderabad.
A number of campaigners and church leaders had campaigned on their behalf.
Speaking after the u-turn, SNP MP Kirsten Oswald said: The fact that the refusal has now been overturned rewards the efforts of Greenbank Parish Church who brought this important issue to my attention - and I am delighted that the twinning project will now be able to go ahead.
"The initial decision to refuse visas to the two Pakistani Christians was simply wrong - particularly with it coming down to the applicants being unable to prove they were wealthy enough to be allowed into the UK, despite the visits being fully funded by the Presbytery of Glasgow."
Good news to end 2016. Common sense decision, after much pushing of PM & Home Office, to allow @churchscotland twinning visit to go ahead. pic.twitter.com/kCuVEWpcMz
— Kirsten Oswald MP (@kirstenoswald) December 31, 2016
A Home Office spokesman said: "It is the responsibility of the applicant to ensure they submit the required evidence to show they meet the financial requirements for the visa category they have applied for.
"Where this evidence is not provided applications will be refused."
@kirstenoswald This is great news. Thank you for your efforts in support of your constituents and our wider goal of strengthening links with Pakistan.
— Church of Scotland (@churchscotland) December 31, 2016
The visitors will travel to Glasgow next month for a week-long stay.
They're being hosted by the Presbytery of Glasgow.
Joint Clerk Bill Hewitt told Premier he was concerned the original ruling could have set a dangerous precedent.
"There are other international conferences planned for the future and if we were only going to allow Christians who had money intro the country then that was going to say a dreadful thing for what kind of country Britain was," he said.
Listen to Bill Hewitt speaking to Premier's Marcus Jones.