Tway fired a 5-under 67 to finish 36 holes at 14-under 130, one shot better than Tommy Armour III, who also carded a 67 at the Rock Barn Golf & Spa.
Tway, 52, is still looking for his senior tour win since joining the circuit two years ago. He shot 10 birdies and a bogey on the par-5 14th hole en route to the 67.
After Armour, the leaderboard gets crowded. Twelve other players were within four strokes of the top on a course that has yielded plenty of low scores so far this week.
Tied for third place at minus-12 were Mark O'Meara (67), James Mason (65), Chip Beck (65) and Mark Wiebe (68).
One shot further back in fourth were Nick Price (66), Jeff Sluman (67) and Mike Goodes (69).