Browne and the rest of the 155-player field had to wait out a weather delay at the start of the round that lasted more than 3 hours. He completed the opening two days of the biggest event in senior golf with a 9-under 133 total at the Inverness Golf Club.
Browne is seeking his first victory on the Champions Tour after winning four times on the regular circuit.
Mark O'Meara, who finished his round just before 9 p.m. local time, had a 68 and was alone in second at 134. Joey Sindelar, Michael Allen and Mark Calcavecchia shared third place at 135.
Calcavecchia, who finished second to Russ Cochran at last week's Senior British Open, shot a 67.
Peter Senior was in sixth place at 136 and those at 137 included Trevor Dodds, Corey Pavin and Kiyoshi Murota. Cochran was in a tie for 16th place at 139.
Defending champion Bernhard Langer, who has only recently returned to action after missing most of the year with a thumb injury, also fired a 139 for 36 holes.