The 18-year-old went to an immigration tribunal in Glasgow with her mother and two brothers to appeal against moves to return them to their native Zimbabwe.
Earlier in the year, Ms Nhengu was told she must go back because her mother Nokuthula Ngazana’s visa application was turned down.
The decision came amid allegations, denied by the family, that Ms Ngazana had wrongly claimed working tax credits.
But at the start of the latest hearing, a Home Office representative said the case would be reconsidered and a "fresh decision will be made in due course".
After the hearing, the family’s lawyer Frances Farrell said: "The family are pleased that the Home Office have withdrawn their decisions and decided to reconsider my clients’ cases.
"The family are hopeful that they will now be granted leave to remain in the UK.
"They want to thank everyone for all the wonderful support they have had."
Ms Nhengu was eliminated from the talent show at the judges’ houses stage.
She lives with her family in Tillicoultry, Clackmannanshire and was allowed to stay in the country as a dependant while her mother studied at university.
But her mother’s visa expired and the family’s application to remain was rejected as they did not meet Home Office criteria.
The family was told last month to leave the UK voluntarily or face deportation.
Despite initially being told they had no right of appeal, the family was given a lifeline after being granted a full appeal hearing before a judge.
The case, an appeal against the refusal of Ms Ngazana’s visa, was expected to be heard before an immigration judge.
Ms Ngazana and Ms Nhengu held hands as they waited for proceedings to get under way.
But a Home Office representative told the start of the hearing he had instructions to withdraw the original decision dating to October 6, over a "technical issue".
The family’s solicitor Ms Farrell said she hoped a fresh decision would be made within weeks, rather than months.