Mize, who in April will celebrate the 25th anniversary of his dramatic Masters playoff win over Greg Norman, came within one shot of the course record at the TwinEagles Golf Club.
Tommy Armour III shot a 61 on this course in 2010.
Mize hit every green in regulation and finished the round with a two-shot lead over Russ Cochran, Kenny Perry and defending Champions Tour player of the year Tom Lehman. Mike Goodes was alone in fifth place at 65 and defending champion Bernhard Langer was part of the group at 66.
Corey Pavin, who won last week at the Allianz Championship, shot a 70 and was tied for 28th.
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