Steven McIntyre, 19, went home and played as normal on his Xbox computer just hours after murdering Jack Doyle in Greenock, Inverclyde.
McIntyre's single stab wound went through Jack's liver, severing two main blood vessels.
After McIntyre was found guilty at the High Court in Glasgow, detectives said Jack's death was "particularly horrific" and they had been determined to track down his killer.
Jack, whose aunt Elaine was murdered in an unsolved case 26 years ago which has featured on the BBC's Crimewatch, died on January 3 this year in the town's Antigua Street, near to where he had lived.
Detective Chief Inspector Duncan Sloan, of Strathclyde Police, said: "Undoubtedly the Doyle family have suffered more than most and our thoughts are with them.
"While Jack's family will never be able to come to terms with the loss of a much-loved son, brother, uncle and cousin, I hope that the conviction today will, in some small way, begin to ease their pain.
"From the outset my officers and I were determined to bring those responsible for this horrific murder to justice and I would like to thank the Doyle family and the community of Inverclyde for their assistance."
During his trial McIntyre claimed he had acted in self-defence, but the jury didn't believe his story.
Jack and his killer met at a party in Antigua Street. The court was told Jack had taken a knife with him which was tucked into the waistband of his trousers and that he had "flashed it" a couple of times.
It was alleged during the trial that at one point Jack left the flat and shouted up, challenging the occupants to a fight.
Seconds later he was assaulted by Steven McIntyre's co-accused Kevin McIntyre, 28, who was also originally charged with Jack's murder but pled guilty during the trial to a much reduced charge of assaulting him.
Kevin McIntyre slashed Jack twice on the right side of his face.
Steven McIntyre then confronted Jack, who had blood pouring from his face, and stabbed him once.
Both men will be sentenced later this month once background reports are available.
Steven McIntyre will be detained without limit of time, but temporary judge Sean Murphy, QC, has to determine how many years detention he must serve before being eligible for parole.
Defence counsel will give their pleas in mitigation at the next court hearing.
Meanwhile, a witness in the trial was jailed for 18 months for contempt of court.
Christopher Woods, 22, had during the course of his evidence at the High Court in Glasgow used abusive language while speaking to prosecutor John Scullion.
Sean Murphy, QC, told him: "Your behaviour was insolent and calculated to be offensive.
"You have also deliberately prevaricated to avoid being in your eyes a grass.
"What you did strikes a blow at the justice system."
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