Omar Sadiq (32) was found seriously injured on Boydstone Road on the afternoon of Tuesday, September 15, after suffering two stab wounds.
He was taken to the Queen Elizabeth University Hospital where he died a short time later.
Hashim Uddin (28) entered his guilty plea when he appeared at the High Court in Edinburgh on yesterday (Tuesday).
He will return to be sentenced on Tuesday, June 22.
Detective Chief Inspector Peter Sharp from Greater Glasgow CID said: “Our thoughts and condolences remain with Mr Sadiq’s family, who have been left devastated by his death.
“I hope this outcome will offer them some comfort, and allow them to move forward.
“Violence of this kind will not be tolerated in our communities, and Police Scotland will always ensure those who commit violent offences are brought to justice.”