The South Korean improvised superbly to head Nani's deflected cross beyond the reach of goalkeeper Wojciech Szczesny.
Wayne Rooney could have doubled the lead when he took a harshly awarded penalty after Gael Clichy had been adjudged to have handled, but Rooney wildly blazed the spot kick over the bar
Arsenal's best efforts fell to Marouane Chamakh, who missed with a header and had a shot blocked by Nemanja Vidic - but it was an ineffective performance from the visitors overall.
Arsenal have failed to beat either Man United or Chelsea in ANY of their last 11 league meetings now - an obvious indicator that the Gunners still have work to do to catch up to these clubs who have split the last six league titles between them.
Top of Premier League Table
Team Pl GD PTS 1 Man Utd 16 +20 34 2 Arsenal 17 +15 32 3 Man City 17 +11 32 4 Chelsea 17 +19 31 5 Tottenham 17 +3 27