The Clarets had kept the away side's dangermen at bay for the majority, but left the South Korean international completely unmarked from Erik Lamela's corner in the 75th minute.
Harry Kane, who flicked on the set-piece to claim another assist, had cleared James Tarkowski's header off the line at the other end moments earlier.
Jose Mourinho's side climbed up to fifth as a result while the Clarets, with a solitary point from five games, remain in the bottom three.
Here are the ratings...
Jose Mourinho's side climbed up to fifth as a result while the Clarets, with a solitary point from five games, remain in the bottom three.