The South Korea star star headed the only goal of the game, celebrating his sixth goal of the campaign, latching onto a deflected ball flighted inside the box from Nani.
Wayne Rooney squandered a perfect opportunity to double United's advantage late in the second half from the penalty spot after Gael Clichy was penalised for a foul on Nani, but the England striker blazed his effort high over the crossbar.
The win, watched at Old Trafford by former United midfielder and England international David Beckham, saw United climb above the Gunners in the league by two points with a game in-hand.
More to follow.
Park life: Ji-sung Park celebrates his match-winning goal with provider Nani to put United top of the league
Heading up: Ji-sung Park did well to create space and direct his looped header into the back of the net
Welcome Beck: Former United favourite David Beckham returned to Old Trafford to watch the game with former team-mate Gary Neville
Over the top: Wayne Rooney failed to double United's advantage in the second-half after smashing his penalty high over the crossbar
Manchester United 1 Arsenal 0: How the action unfolded at Old TraffordWin FIFA 11 signed by Wayne Rooney and an Xbox 360 4GB courtesy of EA SportsMANCHESTER UNITED FC