Grace -- who has led after each round at St. Andrews in Scotland -- grabbed a four-shot advantage, finishing 54 holes at 20-under 196.
The South African has been on top since firing a course-record 12-under 60 Thursday on the Kingsbarns course, following that up with a second-round 67 Friday.
Grace drained three straight birdies on the back nine but then stumbled to a double-bogey on the par-4 15th. He ended the round with a birdie on the 18th.
Thorbjorn Olesen (68) was in second place at minus-16.
Fredrik Andersson Hed (66) and Alexander Noren (65) ended the day knotted for third at 15-under 201.