The campaign for the Bakhsh family, which received support from across the country, was recognised at the annual Herald Society Awards in Glasgow on Wednesday.
Former moderator Very Rev Dr Susan Brown said she was "surprised and delighted" to be given the award.
The Church's campaign led to teenagers Somer and Areeb Umeed Bakhsh, from Possilpark Parish Church, winning a seven-year battle to stay in their adopted home city of Glasgow.
The pair, who have been granted limited leave to remain along with their parents, Maqsood and Parveen until February 2022, feared their lives would be in danger if they were sent back to Pakistan where Christians are persecuted.
Their minister Rev Linda Pollock led the campaign for them to stay.
Praising her work Dr Brown said: "Ours was, and is, a campaign to right what seems so wrong on behalf of one family who are a part of our Christian family.
"We are only doing what family do - standing up for each other.
"The family, linked with the passion of Rev Linda Pollock, started the ball rolling.
"The compassionate and persistent skills of the Church's communications team, alongside partnerships with the local MP and local MSP gave the campaign traction.
"But we still feel that the lovely Umeed Bakhsh family should be given leave to stay in the UK permanently without having to raise fees that are beyond them for future applications."
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.