Cole matched the best round of the tournament to get to 12-under 198, a stroke ahead of Ryan Gerard after he finished a round of 68 with back-to-back birdies. Mac Meissner (67) and reigning US Open champion J.J. Spaun (68) were two strokes back.
After four birdies in his first eight holes, Cole added two more through 11 holes on a 90-degree day at Hogan's Alley, which firmed up in that heat after rain earlier in the week. His only bogey was sandwiched by birdies on the back nine.
PGA Tour rookie Jordan Smith, who entered the day leading at 10 under with a one-stroke lead, had four bogeys without a birdie in a round of 4-over 74 to drop to a tie for 19th place.
Spaun helped his cause as he gears up for his US Open title defence when he birdied with a blast out of a greenside bunker at the 428-yard 15th hole after bogeys on two of his previous three holes.
This is the 120th PGA start for the 37-year-old Cole, whose parents were both former professional players.
His mother, Laura Baugh, was the LPGA's rookie of the year in 1973 and had 70 top-10 finishes over a 25-year LPGA career. Bobby Cole was a native of South Africa whose only PGA Tour victory came in 1977 at Flint Elks Club in Michigan.
Cole, who will be going for a win on his mother's 71st birthday on Sunday, has the 54-hole lead for the first time since his PGA Tour debut in 2021.
"It's not going to be an easy day tomorrow. I know that from my experience," Cole said. "I know that it's going to be difficult, but that's why I practice really hard and that's why I try and do everything the way I do."
The last time Cole played in the final group in the final round was at the 2025 Sony Open, when he finished fifth.
His chip-in from 27 feet off edge of the green at the 196-yard par-3 16th came after the bogey at the par-4 15th. He birdied the 439-yard 14th hole after an approach shot inside 5 feet.
Cole went into Saturday's round at Colonial tied for 25th and five strokes off the lead.
Meissner, 27, who lives in Dallas, had five birdies through 11 holes. He missed an opportunity to go lower with two bogeys on the back nine.
