Norman was at 10-under 200, a stroke ahead of overnight leader Fred Funk (72) and Loren Roberts (67).
Tom Watsons hopes of improving on his runner-up spot in the British Open last week took a hit after a 70 that left him six shots behind Norman.
Watsons putter remained cold, despite an overnight grip change following similar problems on Friday.
Otherwise, I was missing everything. Everything was right, everything pushed. Maybe I ought to aim left.
I dont have very good speed control on these greens.
Norman found the right speed in a solid round.
I put the ball in play and putted decently, he said. I got on the tee and could see the shots I wanted to play and just went and played them. I really wasnt worried about anything else.
The Shark loves the Sunningdale course, where he played often and won during his years on the European Tour.
I feel comfortable around this golf course. I always have done for some reason. I like the way it feels to me off the tee. You can be aggressive or conservative, depending on how you want to play. Today I had a mixture of both.
Funk dropped his first shot of the week at the tough second hole, then double-bogeyed the 12th and bogeyed 14.
The good news is that Im still there. I can still win it,' Funk said. The bad news is that I put everyone else in the tournament right back in it.
Larry Mize also shot a 64, and Bernhard Langer, Ben Crenshaw and defending champion Bruce Vaughan all had 65s. Langer has a share of seventh place four shots behind Norman as he bids for his fifth Champions Tour victory of the year.
I hit a lot of good quality shots even though I didnt make many putts, Langer said. I still shot 65 so Im happy with my long game.
Denis Watson was in fourth place, one ahead of Mize and Sam Torrance, who was second overnight. Torrance triple-bogeyed the tough second hole and shot 71.
Mize birdied four in a row from the 11th, and the last two.
Mize, who 22 years ago made a spectacular chip-in to beat Norman for the Masters, was delighted with his round, which contained six birdies in a back nine of 29.
I felt I got things rolling on the back nine and was able to bring it in pretty good, he said.