The man died after being stabbed in the chest following an argument with a fellow passenger on the 10.10 Virgin train from Glasgow to Paignton in Devon.
Although staff managed to lock the knifeman in a carriage after evacuating passengers, he kicked out a window when the train stopped at Oxenholme station in Cumbria and fled.
The attack caused panic and confusion among the train's 200 passengers, some of whom were treated for shock. It also caused severe delays on the West Coast main line as police scoured the train for clues.
A spokeswoman for British Transport Police said a suspect from Skelmersdale in west Lancashire was later arrested in the Kendal area.
The attack follows a series of incidents that have raised concerns about the level of knife crime, and comes three days after the launch of a national knife amnesty and a month after British Transport Police announced they would use scanners to detect knives at stations.
Officers are being given hand-held scanners as well as portable scanning arches as part of the national roll-out.
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