The former US Open champion, who despite several close calls has endured a barren title run worldwide since his play-off victory at the World Challenge in 2010, fired a flawless four-under-par 68 on Saturday to post a 13-under total of 203.
"I played very solidly again today," McDowell said after sinking two long-range birdie putts early on to maintain his grip on the tournament. "Bogey free is always nice on any golf course.”
McDowell said he was very happy with the way he has been hitting the golf ball.
"It'll be a nice way to finish the year if I can get a good win tomorrow, but there will be a few guys on that board that will have a little something to say about it for sure," he said.
McDowell's closest challenger was first-round leader Keegan Bradley who matched the day's best round with a six-birdie 67 at a rain-soaked Sherwood Country Club to finish at 11 under.
Tournament host and defending champion Tiger Woods, bidding for his fourth victory this year, was a further three strokes back after narrowly missing a seven-foot birdie putt at the last to card a 69.
Woods failed to birdie any of the five par-fives on the hilly course that winds its way below the Santa Monica mountains as he ended the day level with fellow American Bo Van Pelt, who birdied the par-four last for a 70.
"It was wet out there," Woods said about the saturated Sherwood layout after mixing four birdies with a lone bogey.
"It was a little sloppy early, and overall I thought it was tough to get the ball close today.
"I didn't play the par-fives well and didn't play (hole) eight well again. I missed a few opportunities out there. I felt like I played decent enough to get to 10 under, to get to double digits, and just didn't do it.
"As of right now I'm five back. I'm going to have to shoot a low one tomorrow and see what happens."
On a soggy morning, 2010 US Open champion McDowell began the third round with a commanding three-shot lead but that was swiftly trimmed to just one after the fast-starting Bradley birdied two of the first three holes.
However, McDowell got his putter working in scintillating fashion, sinking birdie putts from 30 feet at the par-five second and the par-four fourth to restore his three-stroke advantage.
Though American Bradley picked up another shot at the sixth to apply early pressure on McDowell, the Northern Irishman maintained his grip on the tournament with further birdies at the ninth and 11th before parring the last seven holes.
"It would have been nice to pick a few more (shots) up on the way in, I guess, finishing with seven straight pars when there are some chances out there," said McDowell, who was runner-up on his debut here in 2009.
"I played disciplined golf to some of those tighter pins, couldn't seem to get anything to drop.
"But two shots ahead going into Sunday, I'll take that any week, anywhere, any time. It's right where you need to be," he added.
Bradley, who became the first player to win a major using a belly putter at the 2011 PGA Championship, was delighted to be in a position to win his first tournament since the WGC-Bridgestone Invitational in August.
"I feel really good out there," said the 26-year-old and three-time winner on the PGA Tour. "It's so fun to be back in the hunt again. It's been a while. It's been a few months.
"Graeme loves this place. He just has such an unbelievable record here. I'll be looking forward to playing with him tomorrow. It'll be a good time."
World Challenge leaderboard after third round:
203 Graeme McDowell (Northern Ireland) 69 66 68
205 Keegan Bradley (US) 69 69 67
208 Tiger Woods 70 69 69
Bo Van Pelt 70 68 70
209 Jim Furyk 69 69 71
210 Rickie Fowler 73 67 70
211 Nick Watney 67 73 71
212 Bubba Watson 71 74 67
Steve Stricker 73 71 68
Webb Simpson 70 73 69
214 Zach Johnson 74 70 70
Dustin Johnson 74 68 72
Matt Kuchar 73 69 72
215 Hunter Mahan 71 73 71
216 Ian Poulter (Britain) 73 72 71
Brandt Snedeker (US) 75 68 73
Jason Dufner 73 68 75
Jason Day (Australia) 71 75 72