Gary Reilly attacked Paul McCarroll, 49, in the street in Parkhead, Glasgow, in February last year.
Reilly's partner Lorna Holland - the mother of the victim's child - told a jury how she tried to keep him alive after he had been struck.
The killer was sentenced to at least 19 years after being convicted of murder at the High Court in Glasgow.
The fatal attack happened outside Mr McCarroll's home in the city's Westmuir Street.
The court heard that Reilly, 46, turned up there with a bag of Miss Holland's belongings after she stayed at Mr McCarroll's flat following a row between the men.
The jury heard Mr McCarroll and Miss Holland had previously been in a relationship, but remained "good pals".
The victim went downstairs to speak to Reilly. CCTV caught the pair confronting each other before Reilly stabbed the former bus driver.
Miss Holland, 37, told the court she also eventually went onto the street and sobbed as she recalled tending to Mr McCarroll when realising he was hurt.
She told the court: "Paul was holding onto a pole - he was not really talking to me.
"He was just staring at me...then he slipped down the pole.
"I tried to give him CPR. I was shouting for help from people at a nearby pub.
"I was talking to him about our daughter. I just knew that something was not right and then an ambulance came."
Mr McCarroll never recovered after being rushed to hospital.
Reilly had denied the murder charge. He already had a lengthy list of crimes including a high court conviction for fireraising.
Judge Lady Stacey told him: "You must have had a knife with you when you went into Westmuir Street. You took a man's life as a result of some stupid quarrel."
A man who stabbed his girlfriend's ex-partner to death following a "stupid" row has been jailed for life.