Police say the owner left the car running with the keys inside in Union Square around 3 p.m.
Authorities were able to track it down thanks to an iPhone left inside.
Officers followed the Porsche for about two miles until the driver crashed it into empty cars and flipped over near 50th and Lexington.
Calvin Jones, 40, was arrested on a slew of charges including grand larceny and resisting arrest.
Police say Jones has been arrested twice before for assault.
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