The Co Down golfer's scoring average of 74 in the 'unofficial fifth major' looked set to tumble after the world number two went to the turn in 31 thanks to five birdies and no bogeys.
Starting from the 10th, the 24-year-old birdied the par-five 11th, 12th and 14th to stand three under par approaching the daunting closing stretch.
A pushed drive on the par-five 16th meant McIlroy was unable to reach the green in two, but after pitching to 20ft he rolled in the birdie putt and then struck a superb tee-shot to the island green on the famous par-three 17th.
He converted the birdie putt from seven feet and added a par on the 18th to remain five under par.
That was three shots behind little-known leader Roberto Castro, who had also covered the back nine in 31 and then eagled the par-five second and birdied the fourth to reach eight under par.
Castro was two ahead of Casey Wittenberg with McIlroy and playing partner Steve Stricker on five under, while the third member of their group, Masters champion Adam Scott, was two under.
McIlroy, a two-time major winner, is without a win so far in 2013 after five victories around the world last year.