Tway shot his 63 on the par-71 TPC at The Canyons. Steve Flesch carded his 8-under-par 64 on the par-72 TPC at Summerlin to grab his share of the lead.
The two courses are being used for the opening two rounds, before the TPC at Summerlin hosts the final two rounds.
Former PGA champion Rich Beem and Bubba Dickerson each shot 7-under-par 65. They were joined in third place by Will Mackenzie and Patrick Sheehan, who shot 64s at The Canyons.
Tway played the back nine first on Thursday and was just 1 under through eight holes. He drained a 25-footer for birdie on the 18th, to catch fire. Around the turn, Tway birdied the first and second to make it three in a row.
After a par on No. 3, the 1986 PGA champion again ran off three straight birdies from the par-5 fourth to jump to minus-7. Tway carded his final birdie at the par-4 eighth.
'I'm very pleased. I haven't played well this year, this is my low round of the year, so that is a good thing,' Tway stated. 'I'm going to just keep plugging along.'
Flesch eagled the par-5 third at Summerlin to get his round going. After a pair of pars, he birdied the sixth.
The 39-year-old carded three consecutive birdies from the par-5 ninth to jump to minus-6.
Flesch carded back-to-back birdies from the 15th to move into a share of the lead. He parred the final two holes to end there.
Dickerson was the first in the clubhouse at minus-7. He birdied the second and came right back with an eagle at three. Dickerson made the turn at minus-4 thanks to a birdie on the par-5 ninth.
The 25-year-old drained three straight birdie efforts from the 12th to get to 7 under. Dickerson parred the final four holes to end there.
'I actually feel like I got that spark (Wednesday),' Dickerson admitted. 'I played with a good friend of mine, Eric Axley, who we all know has been playing great. We went at it and I finally got the better of him yesterday for the first time in a while. That gave me more confidence than anything.'
Former British Open winner Todd Hamilton carded a 6-under-par 65. He was joined in a tie for seventh place by Joe Ogilvie, D.A. Points, B.C. Open winner John Rollins, Vance Veazey and Duffy Waldorf, who all carded 65s at The Canyons, as well as Ben Crane and Verizon Heritage champion Aaron Baddeley, who shot 66s at Summerlin.
David Howell, who stands third on the European Tour Order of Merit, shot a 2-under-par 70 at Summerlin and is part of a large group tied for 67th.