On what would have been his 52nd birthday, the family of Lee Pomeroy said he was "an honourable man and would always help somebody who was in trouble".
The tribute comes as neighbours described the moment police swooped on a flat in Willbury Road, Farnham, in the early hours of Saturday morning to arrest a 35-year-old man.
Mr Pomeroy was travelling with his 14-year-old son on the 12.58 service between Guildford and London Waterloo on Friday when he was stabbed several times.
At 6am on Saturday a suspect was arrested on suspicion of murder at a flat near Farnham Hospital alongside a 27-year-old woman detained on suspicion of assisting an offender.
Neighbour Grant Christy told reporters he witnessed the police breaking into the building, taking a couple into custody and leading a young child from the house.
He said: "At six they smashed the door down, woke me up immediately, obviously.
"Initially I just heard the banging. Sounded like someone trying to kick the door in, that's what it sounded like to start with. And then I jumped out of bed, put my ear to the door, listened to what was going on.
"Then I heard the police shouting, 'put your hands up, turn around', all that sort of thing and then it went quiet.
"They led her out first with the kid, barefoot, put her in a police wagon over there, then a few minutes later they pulled him out handcuffed."
In a statement released by British Transport Police (BTP), Mr Pomeroy's family said: "Lee took his son on a trip to London hoping to spend some quality time with him which was cut short by an horrific and pointless attack.
"Lee would have had his birthday today but did not get to see his presents.
"He was an honest, bright person, who loved music very much.
"He knew history and art and he was a bachelor of science in maths.
"He was a devoted family man and did everything for his family.
"He was an honourable man and would always help somebody who was in trouble.
"He was a loving husband and father. He will be deeply missed by all his family."
Estate agent Wendie Thompson, who lives nearby, expressed her shock at the incident and said police had continued to guard the flat.
She told Press Association: "The officers were here when I woke at 8am.
"Police have been active all day - on guard outside the flats.
"I think there were detectives and armed response officers."
The 59-year-old, who has lived in the area for 11 years, said she believes she saw a man matching the description of the suspect on Thursday morning standing in the nearby Farnham Hospital car park using a mobile phone.
She said: "He was noticeable because he was tall, good looking and immaculately dressed in sports wear which drew my attention.
"He fits the description and was a new face here. It was unusual."
Mr Pomeroy and his son boarded the train at London Road station in Guildford alongside the suspected killer, described by police as a slim, black man in his 20s or 30s, who was approximately 6ft tall with a beard.
The men became locked in a three to four-minute row moving through the carriage and into another before this escalated into an "unprovoked, violent attack", police said.
The man fled the train at Clandon station and headed in the direction of Dedswell Drive while the service continued to Horsley station where police and paramedics attended.
A woman who lives in Clandon reportedly told other villagers that she had spoken to a "very sweaty and nervous" man in a field near her home afterwards.
Police said they are not looking for anyone else in connection with the killing.
Detective Chief Inspector Sam Blackburn said officers were "confident to say that this is not believed to be a random assault", adding: "Nothing justified the extraordinary violence that followed and we are concentrating our efforts on the on-going investigation."
Philip Herrington, the Rector of St Mary's Church, West Horsley, visited Horsley station to lay flowers, describing the attack as "lamentable".
On Saturday he told how officers he had spoken to were shocked by what they had seen, adding: "You don't really expect anything like this to happen generally, not in a place like this, not on a midday train."