Durant and Daley shot 68 to match Tway at 10-under 130 at Canyon Meadows.
The 55-year-old Tway had an eagle, seven birdies and two bogeys.
''I putted very well today - probably the best I've putted in 20-something years, so it was kind of fun,'' Tway said ''The greens are some of the nicest greens I've ever putted on. If you hit a good putt, they're going in. Guys are making putts from everywhere.''
He's winless on the 50-and-over tour after winning eight times on the PGA Tour, including the 1986 PGA Championship.
''I know I can play better than I have,'' Tway said. ''I haven't done it, but I keep trying to do it. If I just keep enjoying it, then it doesn't really matter. I fully should play a lot better than I play, but I haven't. You either keep working at it or go home and I'm going to keep working at it.''
Durant is making his eighth Champions Tour start since turning 50 in April. He also has three top-25 finishes this season in 15 PGA Tour starts.
''I know there's three of us tied, but by the time we get on the first hole there might be guys who have already passed us,'' Durant said. ''That's how bunched it is. It will be quite a shootout tomorrow, and if the weather's good there will be a lot of birdies flying.''
Daley won the 2012 Senior Players Championship for his lone tour victory.
''You have to be very much on your game and even more so than you might even think,'' Daley said. ''But you also have to prepare in a lot of different ways in your mind and physically for what you have to go through to compete against these guys because these guys, well, they've been whooping me for decades.''
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.
''I would rather be chased than chasing, but I don't have that option,'' Langer said. ''Hopefully, your swing is good enough and your putting stroke allows you to do what you need to do.''
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.