The Holywood golfer finished with a string of birdies on four of his last six holes to finish with a two-under-par 69 on Sunday.
It left him on seven under for the tournament and six shots behind winner Tiger Woods.
McIlroy was two over after his first nine holes with a birdie at the second hole followed by bogeys on the sixth, eighth and ninth.
However he went on to card birdies at 13, 15, 16 and 17 to make amends on the back nine.
Padraig Harrington was well off the pace with a final round of 76 while Graeme McDowell missed the halfway cut.