Glasson, 52, who has undergone 25 surgeries in a span of 26 years, is looking for his first title on the Champions Tour.
He finished 36 holes at the Shoal Creek Golf Club in 9-under 135 after posting a 69 in the second round.
Reigning Senior British Open champion Russ Cochran shot a 68 to move into second place by himself at 137. Defending champion Tom Lehman was part of a tie for third at 138 along with Jeff Sluman, Brad Bryant and Fred Funk.
This is the first time Glasson has had the 36-hole lead on the Champions circuit. The last time he was in this position on the PGA Tour came in 1997.
Roger Chapman, who won the year's first major title at the Senior PGA Championship, was tied for 38th place at 147.