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Tway, 47 and the 1990 winner, shot an 8-under 63 on the 7,019-yard TPC Canyons course that plays to a par of 71, while Flesch, 39, posted his 8-under 64 on the 7,243-yard, par-72 TPC Summerlin in an event in which.
players alternate between the two courses for the first two days of the tournament, but play the final two rounds at Summerlin.
Four more Americans - Bubba Dickerson, Rich Beem, Will MacKenzie and Patrick Sheehan - are tied at 7 under, a shot behind the leaders in joint 3rd place while a further eight players, including Joe Ogilvie, are at 6 under.
England's Greg Owen kept himself in contention as he lead the European charge with a five-under 66.
Five birdies at the third, sixth, 13th, 15th and 17th left him three shots off the lead.
Fellow countryman David Howell was two under par for his first round, as was fellow Englishman Brian Davis.
Three-time Las Vegas winner Jim Furyk was also 3 under after a 68 at TPC Canyons and defending champion Wes Short Jnr., who beat Furyk on the second playoff hole last year for his only PGA Tour victory to date, opened with a 68 at TPC Summerlin.
Tway teed off to a slow start at the 10th at TPC Summerlin.
"I was just plugging along, but the I made a nice birdie on the 18th hole, nailing a 25-footer, and from there, I started making a lot of putts, which I haven't been doing much this year."
Tway reached the turn in a 2-under 33, then birdied five of the next six holes and finally added another birdie on No. 8 during his bogey-free round.
Flesch was also bogey-free, but jump-started his round when he rolled in a 35-foot eagle putt on No. 3 at Summerlin.
He felt it was a matter of continuing his good form of recent weeks, when he tied for 12th in the Valero Texas Open and for third at Greensboro.
"I'm just kind of riding the wave of momentum," said the 39-year-old.
Tway, a former PGA Championship, has struggled this year and is 176th on the money list, with just $264,701. He finished 69th last season with $1.072 million.
"I just haven't played well," he said. "I've been monkeying around with my swing, as usual. I'm just trying to get better. At times, I see some good things, but I haven't put four good rounds together.
"I keep messing up. But not today."
Winless since the 2003 Canadian Open, Tway hasn't let his lack of success this year get him down.
"I've been out here for an awfully long time and I've been through all kinds of stuff, but I still enjoy working at the game and trying to get better.
David Duval, another former Major winner struggling to get better wasn't able to do so on Thursday. He shot a 2 over 74 and looks headed for the cut.
THE TOP 30 ON DAY 1:
(TC - Canyons par 71, TS - Summerlin par 72)(
-8 Bob Tway (TC) 63, Steve Flesch (SM) 64
-7 Bubba Dickerson (SM) 65, C Patrick Sheehan (TC) 64, Rich Beem (SM) 65, Will MacKenzie (TC) 64
-6 Aaron Baddeley (SM) 66, John Rollins (TC) 65, Ben Crane (SM) 66, C Duffy Waldorf (TC) 65, Joe Ogilvie (TC) 65, Vance Veazey (TC) 65, Todd Hamilton (TC) 65, D.A. Points (TC) 65, C Scott Piercy (TC) 66
-5 Charley Hoffman (TC) 66, Bubba Watson (SM) 67, Fred Funk (TC) 66, Arjun Atwal (SM) 67, Kris Cox (SM) 67, Mark Wilson (TC) 66, Kevin Sutherland (SM) 67, Greg Owen (TC) 66, Todd Fischer (TC) 66, Dicky Pride (SM), Troy Matteson (SM) 67, Paul Azinger (TC) 66, Bill Glasson (TC) 66, Tom Pernice, Jr. (TC)66, Mike Sposa (SM) 67, J.B. Holmes (TC) 66
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