McIlroy felt he still had a chance of claiming a first green jacket if he could match, or better, his lowest score in the Masters, a 65 in the first round having seemingly set him on course for victory in 2011.
However, after making a birdie on the par-five second, the four-time major winner three-putted the fourth from 95 feet and had to scramble to save par on the next two holes.
The odds were against McIlroy joining Gene Sarazen, Ben Hogan, Gary Player, Jack Nicklaus and Tiger Woods in winning all four majors, with Art Wall in 1959 the only Masters champion to start the final round outside the top 10.
McIlroy began the day in a tie for 11th and although a birdie on the par-five eighth took him into red figures on one under par, that was seven off the pace being set by Ryder Cup team-mate Sergio Garcia.
Garcia, who shared the overnight lead with Justin Rose, had birdied the first and third from close range in pursuit of a first major title at the 74th attempt, fittingly on what would have been the 60th birthday of the late Seve Ballesteros.
Unsurprisingly, Ballesteros and fellow two-time Masters champion Jose Maria Olazabal were Garcia's idols growing up, with Olazabal sending his fellow Spaniard a good-luck message on the eve of the tournament.
Rose became the first English winner of the US Open for 43 years at Merion in 2013 and added Olympic gold in Rio last year, but had to settle for three opening pars.
American Rickie Fowler was three shots off the lead on five under, with 2015 champion Jordan Spieth another two strokes back after surprisingly dropping shots on the first and third, either side of a birdie on the second.