Price's round was highlighted by a near-eagle on the par-5 15th hole, where he hit a great fairway wood shot to within 12 feet of the pin but missed the putt, settling for a birdie to get to 11-under par at Glen Oaks Country Club in West Des Moines, Iowa.
Price ended at 10-under 132, knotted with first-round leader Armour, who shot a 2-under 69 Saturday.
Don Pooley also fired a 65 in the second round to claim sole possession of third place at minus-9.
Bruce Vaughan (66), Dan Forsman (68) and Russ Cochran (68) ended the day tied for fourth at 8-under 134.
Swim Week Miami Beach 2014 [PHOTOS]