The 16-year-old victim suffered serious injuries after being attacked in a lane next to Bannerman High School in Baillieston at about 22:30 on Friday.
He had been approached by a young man as he walked through the lane towards Glasgow Road.
Police said he was stabbed following an altercation with the suspect.
The suspect, who was with a young woman, ran off in an unknown direction.
The victim managed to make his way to Maxwell Avenue where an ambulance was called. He was taken to the Glasgow Royal Infirmary where he remains "serious but stable".
The suspect is described as about 18 years old. He was wearing a dark hooded jumper and dark jogging bottoms.
Det Sgt Willie Downie, from Shettleston CID, said: "This teenage boy could have lost his life as a result of this brutal attack and it is critical that we trace the person responsible as soon as possible.
"The surrounding area is popular with groups of youths and I would appeal to anyone who was there around the time of the incident to get in touch.
"In particular I would like to speak to the young woman who was in the company of the suspect as I believe she may have tried to break up the altercation.
"Somebody must know something and anyone with information is asked to contact Shettleston CID on 101.
"Alternatively you can call Crimestoppers on 0800 555 111 where details can be given in confidence."
Police are treating the stabbing of a teenager in Glasgow as attempted murder.