The 20-year-old had fallen at Cavehill Country Park, Belfast, on Tuesday.
David McCrum and Richard Lamont raised the alarm after finding a handbag the next day.
"She was in a hole which, I imagine, saved her life as that kept her from going into hypothermia," said Mr McCrum.
The Queen's University student told the joggers she had been there since about 15:00 GMT on Tuesday.
"She said a gust of wind took her," Mr McCrum said.
"The cold air was passing over the top, she was a very lucky girl."
Mr McCrum said he and his friend found a handbag during an early morning jog and, after returning to the scene, discovered a coat and a hat, which made them increasingly concerned.
"I looked down to see roughly where she fell and I heard a voice saying 'hello'," he added.
"I came across her and couldn't believe it.
"I was amazed, it was unbelievable."
Mr McCrum said he talked to the woman about her family to keep her mind focused.
"I had a connection there, whenever I was looking at her face and into her eyes - looking at someone that was gripping to life," he said.
"It was touching, all sorts of emotions were going through my head."
The woman was taken from the mountain by helicopter on Wednesday and is now in a stable condition in hospital.
Two joggers who helped rescue a German student who lay for 25 hours at the bottom of a cliff have said she is lucky to be alive.