Emmanuel Honiss (17), of Invercargill, spent Saturday night in an old musterer's hut on the mountain range after becoming separated from his family while they were on a four-wheel-drive trip.
Gerard and Katherine Honiss and their sons, Emmanuel and Joshua (16), were in their vehicle when it became stuck about 4pm.
They were within cellphone coverage, and called police about 6.45pm after attempts to free the vehicle failed.
All but Emmanuel had stayed with the vehicle - he tried to walk out before help arrived.
"It appears he took a wrong turn and got himself lost," Constable Jape Wanoa, of Roxburgh, said.
As night was falling, the other three family members were towed back down the hill in their vehicle to Roxburgh, where they stayed overnight.
A search began on Sunday morning for Emmanuel.
New Zealand Land SAR adviser for the Alexandra area Adrian Dance said a helicopter from Wanaka was used to search for the missing teenager.
Several four-wheel-drive SAR vehicles were also put on standby in Alexandra.
The youth was eventually spotted in the Fraser basin area on Sunday morning. After staying in the hut overnight, he had tried to walk out at daylight.
After he was found about 9am, he was flown out by helicopter.
Const Wanoa said Emmanuel was not injured, although had he remained on the mountain range any longer he could have developed hypothermia.
"We had a debriefing about this with the family. They should have stayed together as they were in cellphone range."
