Perry's performance put him at 10-under-par 203, two strokes ahead of the field after 54 holes. The 52-year-old Kentucky native is seeking his first major seniors tour title.
Grabbing sole possession of second place at Bellerive Country Club was Jay Haas, who posted a 4-under 67 to pull in at 8-under 205.
Second-round co-leader Russ Cochran, meanwhile, settled for a 71 to wrap up Round 3 at 7-under.
Rod Spittle (67) took over fourth place at 6-under while Kohki Idoki (68) and Peter Senior (69) followed at 5-under after Saturday's round.