Gallacher, began the day four behind Rory McIlroy (69) and three behind Brooks Koepka (70). He was looking out of sorts and contention for the first eight holes with seven pars and one bogey.
Then something fell in place from the ninth, which he birdied to turn in even par 35. On the back stretch, he birdied seven times and eagled the par-5, 13th to return a record-equalling nine-under 27 and a card of nine-under 63 to get 16-under 200.
The only Indian left in the field, Shiv Kapur (70) is 47th after a round that had four birdies and two bogeys. At 11 shots behind the leader and lying in tied 37th place, Tiger Woods will require a never-done-before performance to win a third time, after he carded 72 which left him on five under par.
After finishing fourth in his maiden appearance in 2000, he has missed the cut only twice in the next 13 years. A year ago, Gallacher cracked a 10-under 62 in the third round after a 63 in the first and moved into a three shot lead ahead of the final.