Darren Pencille and Lee Pomeroy got involved in a heated dispute on the train between Guildford and London on 4 January.
It ended with an "unrelenting" and "savage" attack on Mr Pomeroy, who was stabbed 18 times.
Pencille, 36, of no fixed address, had denied murdering Mr Pomeroy, saying he acted in self-defence. He was sentenced to life behind bars with a minimum term of 28 years.
Pencille's partner Chelsea Mitchell, 28, who picked him up and bought hair clippers and razors for him to change his appearance, was found guilty of assisting an offender by a majority of 11-1. She was sentenced to two years and four months in jail.
Detective Chief Inspector Sam Blackburn said Pencille had a history of violence and a string of previous convictions, including one in 2010 for stabbing a man in the neck during another row.
Pencille's "conviction in 2010 was almost like a mirror, apart from it not being on a train", Mr Blackburn said.
"He's a dangerous man," the chief inspector continued, adding that Pencille had a "propensity for carrying knives".
Pencille also had a "fascination with knives" which officers saw "on his mobile phone, which we seized during the course of the investigation".
Pencille had never never shown any remorse or taken any responsibility for what he had done, Mr Blackburn said.
In a statement read to the court, Mr Pomeroy's widow Svetlana said she missed her husband "every day" and had lost her "friend, my soul mate and my guide".
She added that Mr Pomeroy, who would have celebrated his 52nd birthday the day after he was killed, was bought cards and presents "he never got to see".
There has been a financial impact too because "Lee was the main breadwinner".
During the incident in January, witnesses said they heard both men taunting each other but CCTV of the train carriage had no audio, so it is not known what was said between them.
The court heard that Pencille left the carriage after an exchange, repeatedly asking to be left alone, but was followed by Mr Pomeroy.
Defence lawyers claimed Pencille was blocked at the end of the carriage with no exit route by a much larger man.
Mr Pomeroy's teenage son, who was travelling with him but was in a different carriage during the stabbing, told the court: "My dad is very menacing because he is tall. The guy was taller than me, shorter than my dad.
"Normally when someone says something to my dad he won't let it go."
Kayleigh Carter, another passenger on the train, had described Mr Pomeroy as being "stern, stubborn and patronising" to Pencille.
One witness, Christopher Fieberg, told the court: "The black gentleman was telling the white gentleman to 'leave me alone'," adding Pencille also said he was "hearing voices".
Pencille's mental health was described by his lawyers as "the elephant in the room" but Mrs Justice Cheema-Grubb told the jury that Pencille's mental health "does not help establish a defence of diminished responsibility".
Pencille's mother, Ingrid Robertson, told the court her son had been told in his 20s that he was a paranoid schizophrenic and that he "always thought people were looking at him or wanted to do something to him".
A medical report said Pencille was in hospital a number of times for mental health issues between 2004-2018 and had been prescribed medication for depression, anxiety and psychotic disorders. However, there was no trace of these in his urine after the attack, a toxicologist said.
The Old Bailey heard that Mr Pomeroy was stabbed in the neck and suffered 18 knife wounds during an assault that lasted little more than 25 seconds. He suffered wounds to his neck, torso, thigh and arm.
Justin Rouse QC, defending Pencille, described the fast-moving argument and equally swift and frenzied attack as like "a cat with a mouse".
He said: "If Lee Pomeroy had just stopped and walked away, it would have all been over. One of them was enjoying themselves and one was truly frightened."