Aysan, 22, and her brother Armin, 15, fled Iran in fear of religious persecution and domestic violence in 2018 and have been living in Glasgow since January.
The pair were previously told they would not be able to claim asylum in Scotland and were given 72 hours' notice for deportation last Monday.
The home office now says it will hear their case.
The Christian siblings have been attending Castlemilk Parish Church since February and were both baptised there in June.
Parish Deacon Paul Cathcart, who has been campaigning for the asylum seekers to stay, told Premier the home office's decision is great news.
"We're absolutely delighted, it's more than we could ever have hoped for.
"When we first began the process of trying to have the home office have another look at this case, we had hoped that they would review it but to have the outcome that we've had has just been absolutely brilliant."
Cathcart said the media campaign launched by the Church of Scotland to contest the deportation garnered a lot of support and publicity which he thinks may have contributed to the government's decision to hear the case.
During an interview with the home office, Aysan asked an official "Why are you sending me back to certain death in Iran?"
Cathcart attended the interview with her and said: "She would be stoned to death for committing apostasy. She's terrified to go back and thinks there would be no life if she was to go back to Iran."
The Church of Scotland are hopeful that these latest developments will at least delay the siblings' deportation for a few months, if not years.
Cathcart said the local church community has stepped in to provide help and encouragement to Aysan and Armin throughout the process.
"I've been accompanying them to appointments and trying to keep them reassured that there are people praying for them, that there are people there to support them, they've been coming to worship on a Sunday and people have been asking what practical needs they can help with."
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