Shiromini Satkunarajah, 20, had been taken to a detention centre after being refused asylum.
She was supposed to be on a plane on Tuesday, but 30,000 people signed a petition, Arfon MP Hywel Williams said.
The Home Office said she could stay on an "exceptional" basis.
Miss Satkunarajah was born in Sri Lanka, but fled conflict there with her parents when she was 12.
While her father has since died, Mr Williams said she and her mother have been "battling through the bureaucratic process to get the right to stay".
This has involved attending Caernarfon police station every week while she studies for an electrical engineering degree  - which was where she was detained in a cell for three days.
Mr Williams added others "overstay for years", but Miss Satkunarajah was "picked up" for doing what the authorities asked of her.
Speaking to BBC Radio Wales' Good Morning Wales programme, he said: "They are picking off the easy ones because they are following the rules.
"She was easy to identify as was her mum. She turned up (at the police station) and they took her away."
But he pointed to a "huge wave of support", saying more than 30,000 people signed a petition and letters were written by prominent figures.
In the House of Commons on Tuesday, Mr Williams accused the Home Office of "dithering", criticising it for failing to give the case timely consideration.
An 11th hour reprieve followed.
"In the light of the circumstances of this case, the immigration minister agreed that both Miss Satkunarajah and her mother should be allowed to stay in the UK on an exceptional basis while Miss Satkunarajah completes her studies," the Home Office said.
She is due to finish the course this summer, with Mr Williams saying she is predicted to get a first class honours degree.
Solicitor Raja Rajeswaran Uruthiravinayagan has now got involved in the case after public attention over the weekend.
"We were in the process of filing an emergency judicial review when we got indication the deportation had been deferred," he said.
"Shiromini and her mother have only been released on 'temporary admission'.
"This doesn't mean she's been given formal leave to stay in the UK. What we have to do now is send a pre-action protocol letter to the Home Secretary and give her 14 days to reply and consider the decision."
NUS Wales deputy president Carmen Smith said she was "overjoyed" by the decision.
She added: "I remain of the steadfast view that deporting Shiromini would have been an absolutely disgusting thing to do.
"It is imperative that we value people, their skills, experiences, and cultures, whoever they are and wherever they come from."
A Bangor University student threatened with deportation was "picked off" because she was "following the rules and easy to identify", her local MP said.