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The Northern Irishman had been three clear following two rounds of 67, but a third round 71 reduced the former US Open Champion’s advantage to one after World Golf Championships debutant Hiroshi Iwata posted a 68.
On 11 under McDowell lies one shot ahead of Iwata, who birdied the last from 20 feet, with US Open Champion Martin Kaymer and Masters Tournament winner Bubba Watson tied for third on nine under.
“I played reasonably solid today,” said McDowell, after carding three birdies and two bogeys. “I thought conditions were a little bit more difficult, colder, obviously a little bit of overnight rain made the golf course play a little bit longer.
“I was generally happy with the way I hit the golf ball. I didn't quite score as well as I did the last couple days but I gave myself some confidence from a ball-striking point of view that I can get the job done tomorrow.
“Let's be honest, I had a three shot lead overnight and it's only one now, but I'll take this position any week that you offer it to me, a one shot lead going into the last round, on a golf course that I enjoy; I’m looking forward to the opportunity tomorrow.
“I felt maybe a tiny bit negative coming in, but when I went back and thought through my round, it was difficult.”
Watson had been McDowell's closest challenger when he birdied the second and third and then almost holed his approach to the 603 yard eighth hole for an albatross, but missed the eagle putt from five feet and had to settle for a birdie.
The left-hander then made a costly mistake on the tenth when his simple approach to the green plugged in a bunker, from where he could only blast out to 40 feet and three-putt for a double bogey.
But after dropping another shot on the 12th, Watson birdied four of the last five holes, marred only by a three-putt bogey on the 17th.
McDowell admitted he had never heard of nearest challenger Iwata before this week, but the World Number 127 revealed he is quite well known in his native Japan.
"I'm kind of relatively short tempered, so I always focus not to get too angry at myself," Iwata said. "I believe I'm doing pretty good at that at the moment, so I just want to keep that going."
Asked if he usually got angry quickly, Iwata added: "I'm pretty famous for that in Japan."
US Open Champion Kaymer could be McDowell's biggest threat given his record at the venue, the German shot a closing 63 on his way to victory three years ago and also holds the course record of 62.
"Finally I could make some putts today, that was nice," the 29 year old said after a best-of-the-day 66. "The first two days I played really well but the putter was a little cold.
"Today I make a couple mid-distance putts, only one bogey so I think I put myself in a good position.
"Obviously you need a little help from Graeme in order to win, but I'm playing really well and that's all I can do."
World Number Ten Rickie Fowler and South African Tim Clark are three off the lead on eight under par, with last year's runner-up Ian Poulter and Denmark's Thorbjørn Olesen another shot back. Poulter had been in second place at halfway but could only manage a third round of 72.