Police say the 45-year-old victim and suspect got into a verbal dispute while riding the train on Wednesday around 10 a.m.
The fight spilled onto the platform where the victim was stabbed twice in the back.
He was taken to the hospital where he was said to be stable.
Police say the victim's jacket potentially saved his life.
Police also confirmed the victim is homeless and has at least 16 prior arrests.
The suspect boarded a Brooklyn-bound L train and fled the station.
From January through September, there have been 43 felony assaults on transit systems across the city. That's a 4.4% decrease compared to the same time last year.
A knife was recovered at the scene. Police say they are looking for a man last seen wearing a camouflage court.
The stabbing remains under investigation.
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