The reprieve Hussain, sentenced to hang for killing a seven-year-old boy in Karachi in 2004, came just hours before he was due to face the gallows around dawn at a prison in the city.
It was his fourth stay of execution in five months in a case that has prompted grave concern among international rights campaigners and the United Nations.
Hussain's lawyers and family claim he was under 18 at the time of the killing, and therefore is not eligible for execution under Pakistani law.
They also claim he was tortured into confessing.
His brother Manzoor Hussain said relatives gathered in Muzaffarabad, the main town of Pakistani Kashmir where the family hails from, to keep a vigil during the night of the expected hanging.
"When we were informed at 3:00 am that he has survived, we felt a wave of life inside us," he told AFP.
"We were not expecting this, we had even found a place for his grave in a local cemetery here in Muzaffarabad."
Hussain's elderly mother Makhni Begum said she had faith that God would spare her son.
"My heart says that my son is innocent. We spent the whole night awake, we received a call at the last moment to say the execution has been postponed," she told AFP in Muzaffarabad.
"I bowed to God after this phone call. Now my heart is satisfied that if he is surviving like this, God will save his life."
Sindh prisons inspector Nusrat Mangan confirmed early Tuesday that the hanging -- first scheduled for January -- had been postponed.
The Supreme Court is to examine the questions around Hussain's age, which his supporters have put at 14 or 15 at the time of the offence.
The court met lawyers in the case briefly on Tuesday morning and arranged a detailed hearing for Wednesday, a member of Hussain's legal team told AFP.
Rights groups including anti-death penalty campaigners Reprieve and Amnesty International had pleaded desperately with the government not to carry out the execution.
Hussain's brother Gul Zaman, who had waited anxiously outside the prison for news of the hanging, told AFP the reprieve was down to pressure from media and rights groups.
Hussain's true age has proved difficult to ascertain -- exact birth records are not always kept in Pakistan, particularly for people from poor families like Hussain's.
The UN estimates that only around a quarter of births in Pakistan are officially registered, one of the lowest rates in Asia.
A birth certificate for Hussain circulated in the media several months ago, but it appeared to have been issued only in December and Interior Minister Chaudhry Ali Nisar Khan said there was no proof of its authenticity.
The Federal Investigation Agency carried out a probe into his age earlier this year and found he was an adult at the time of his conviction -- though the results have not been published officially and Hussain's supporters say the investigation was flawed.
In an open letter on Sunday, Amnesty International, Human Rights Watch and Reprieve urged President Mamnoon Hussain to grant Hussain clemency.
The letter said Hussain had been coerced into confessing with beatings, electric shocks and cigarette burns.
The campaigners also said Hussain's lawyer did an inadequate job at his trial, failing to bring up important evidence or raise the question of his age.
Pakistan has hanged more than 130 convicts since restarting executions in December after Taliban militants murdered more than 150 people at a school, most of them children.
A moratorium on the death penalty had been in force since 2008, and its end angered rights activists and alarmed some foreign countries.
The Hussain case has drawn particular concern, with a panel of UN rights experts calling on Friday for his hanging to be halted.
Hussain, the youngest of seven children, was working as a watchman in Karachi in 2004 when a seven-year-old boy went missing from the neighbourhood.
A few days later the boy's family received calls from Hussain's mobile demanding a ransom of Rs0.5 million, according to legal papers.
Hussain was arrested and admitted kidnapping and killing him, but later withdrew his confession, saying he had made it under duress.
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