Anthony Kim shot an 8-under 62 Saturday to take a one-stroke lead after the third round of the Greenbrier Classic.
Simpson was the second round co-leader with Brendon de Jonge. De Jonge shot 72 to fall five strokes behind.
Kim's best round of the year left him with a chance to earn a spot in next week's Bridgestone Invitational with a win. His last win came a year ago at the Shell Houston Open before he underwent thumb surgery and took three months off.