Durant and Daley shot 68 to match Tway at 10-under 130 at Canyon Meadows.
The 55-year-old Tway is winless on the Champions Tour after winning eight times on the PGA Tour, including the 1986 PGA Championship. He had an eagle, seven birdies and two bogeys.
Gary Hallberg, Mark McNulty and David Frost were 9 under. Hallberg shot 65, McNulty 66, and Frost 68. Bernhard Langer, the tour leader with five victories this season, topped the group at 8 under after a 65.
Tom Pernice Jr. and Bart Bryant, tied for the first-round lead after matching the course record of 62, struggled in the second round. Pernice had a 70 to drop into a tie for seventh at 8 under, and Bryant shot 71 to finish at 7 under.
Defending champion Rocco Mediate was tied for 16th at 6 under after a 66. Mediate won the inaugural tournament by seven strokes, shooting 63-64-64 to match the tour record for fewest strokes in a 54-hole event.
Fred Couples also was 6 under after a 66.