Vaughan birdied the par-3 eighth to take a three-shot lead at 7-under, but then bogeyed four straight and Cook rolled in a 4-foot birdie at 13 for a two-stroke lead at Royal Troon.
The 50-year-old Cook, who was runner-up to Nick Faldo at the British Open at Muirfield 16 years ago, goes into Sunday's final round at 6-under 207, leading Vaughan by one shot as he chases his first major on the Seniors tour.
"It's not that it would redeem , but it would certainly help in my way. I won 11 times on Tour and that's not bad. I didn't capture a major unfortunately. I had a few chances I didn't capitalize on and that part is missing. I feel incomplete without having a major."
Vaughan came back with a birdie at No. 18 for a 69 and was one stroke ahead of Eduardo Romero, who had a 68. Tom Watson and Bernhard Langer both shot 71 and were another three shots back. Greg Norman, who had a bogey-free 67, was tied for sixth at 1-over 214.
"I know that there are a lot of tournament winners behind me, a lot of good players and that's what you want," Cook said. "I came over here to win this championship and if I do the things that I'm supposed to know how to do. You have to be patient and hit quality golf shots tomorrow and let it fall where it falls."
Norman was unhappy that he didn't get any breaks on the green, despite tying his best round of the championship so far. Starting the day eight shots off the lead, Norman picked up three in the first nine when he birdied the first, fourth and sixth holes. He made another birdie at 16, but said his score should have been lower.
"Not very happy to tell you the truth," said Norman, who nearly became the oldest winner of a PGA Tour major last weekend at the British Open. "There wasn't anything wrong with my game today and I even felt like I putted great, but didn't make anything and I'm very disappointed.
"If you're playing well there are some shots you have to be aggressive with today, and I was. I hit them great. I didn't capitalize on my round. It was really the worst score I could have shot."
The sun shone for the third day running at these links on the west coast of Scotland, but the wind changed direction for the third time.
"We have played three completely different conditions," Cook said. "This was another different golf course."
Vaughan, who was tied for the lead after the opening round, blamed himself for dropping four shots around the turn.
"I hit the wrong club off the tee [at the ninth] and had to chip out, I missed a short putt at 10, hit a bad shot at 11. At 12 I hit a good shot, but got the wrong yardage and I tried to chip it up but it flew clear over [the green] by 30 yards."