His counsel, John Fraser, said he was not seeking name suppression.
Police prosecutor Sergeant Rob Mills said Singh was hitchhiking north on State Highway 94 on Monday. He was picked up at Lumsden and dropped off at Balfour. At the intersection of SH94 and Queen St, he hid his backpack in bushes and walked into the town.
Outside a dairy he saw the Mazda, which had been left outside the shop with the keys in the ignition while its owner went in to buy lunch.
Singh took the car and returned to get his backpack.
When he noticed the baby asleep in his car seat in the back he removed the child from his seat, placed him on the side of the highway, retrieved his backpack and drove off at speed.
A passing truck driver and the boy's mother both saw him leave the baby on the side of the road, Sgt Mills said.
Police chased Singh in a marked patrol car with lights and sirens on but he failed to stop.
He turned down a no-exit gravel road leading to the Mataura River, and when the road ran out, drove across paddocks before losing control of the vehicle and going over a small bank.
Singh ran off along the river but was soon caught by police. The cellphone was in his jeans pocket, Sgt Mills said.
When interviewed by police, he said had stolen the car intending to drive to Dunedin and did not know the child was in the car when he did so.
He estimated he had reached speeds of 200kmh during the chase.
Judge Michael Turner convicted Singh and remanded him in custody for sentencing on December 13.