The 34-year-old from Phoenix hit an eagle at the par-five fourth and recorded four birdies at the fifth, ninth, 11th and 12th holes in a mistake-free round on a low-scoring day when forecast bad weather at the Hamilton G&CC in Ontario never materialised.
He leads on 16 under, ahead of William McGirt, with Scott Piercy, who shot a 62 in the first round, another shot behind.
United States players filled the top 10 places at the end of the third round.
Garrigus was pressed continually by McGirt and Piercy who around the turn joined him in a three-way tie for the lead.
Piercy dropped shots at the 10th and 13th, although he recovered with birdies at the 15th and 17th.
McGirt, too, bogeyed the 13th before taking a birdie at the 16th.
Scott Stallings, Chris Kirk and Bo Van Pelt finished tied for fourth place on 12 under after Stallings and Kirk both shot seven-under par 63s.
Kirk hit seven birdies in eight holes between the third and the 10th in a flawless round and Stallings scored three birdies and an eagle at the 10th before dropping his only shot three holes later.
Van Pelt made a bogey at the first but recovered with four birdies in his round and no other dropped shots.
South Africa's Retief Goosen matched Stallings' and Kirk's best rounds of the day with a 63 that included seven birdies and no dropped shots to take him 42 places up the leaderboard into a tie for 11th.