Scott's round included seven birdies and two bogeys on the TPC at Las Colinas course, while Lowery played bogey-free at the Cottonwood Valley Course. Their lead is one shot over Bob Estes and Brett Wetterich, who both shot 66s at Cottonwood Valley.
The first two rounds are split over both courses, with the weekend being hosted by the TPC at Las Colinas course.
Scott began his first round with a birdie on the par-4 first hole at Las Colinas, knocking a pitching-wedge within 12 feet to set up the putt. After five consecutive pars, he carded three straight birdies from the seventh to get to 4 under around the turn.
At the par-5 seventh, Scott chipped within a foot to set up his second birdie of the day. He then made putts of 30 and 8 feet at the next two holes.
Scott dropped his first shot at the par-4 12th when he three-putted from about 18 feet. He got that stroke back with a birdie at the par-3 13th, knocking a 7-iron within a foot, but stumbled to another bogey at the 14th, where he needed three putts from 45 feet.
'Unfortunately I had a couple three-putts, but I made up for that with some other good putts, too,' Scott said.
Settling down after that stretch, Scott reached 5 under with birdies at 16 and 18, finishing his round with a 12-foot birdie putt at the last.
'Considering it was a little windy out there, I'd say it was a very good round of golf and a nice start to the week,' Scott said.
The 25-year-old, three-time PGA TOUR champion has held at least a share of the first-round lead only once before -- at the 2004 Players Championship, which he won. This is his first time playing the Byron Nelson.
'It always fell on the wrong week unfortunately,' said Scott. 'I'd be going back to Europe now because the European Tour this week moves back into Europe, so I'd always be starting to play over there. This one just fell a little too early for my run coming for the U.S. Open or whatever it may be.'
Also beginning his round with a birdie at the par-4 first hole, Lowery breezed through Cottonwood Valley with just 26 putts -- seventh-best on the day. He added two more birdies on the front nine -- at the par-4 seventh and the par-3 ninth -- to make the turn at minus-3.
Four straight pars followed, and Lowery picked up another stroke with his fourth birdie of the round at the par-4 14th. He reached 5 under with a birdie at the par-5 16th.
Lowery, 45, has more experience than Scott holding at least a share of the first-round lead. This is the 17th time he has done so, though he has only won once before in this position.
'I played solid and putted well, which kept me in there when I wasn't hitting the greens,' said Lowery, who ranked 19th in greens in regulation percentage.
Among the top-22 players on the leaderboard Thursday, just seven played their first rounds at the TPC Las Colinas course.
That figure matches with recent history here, as those who start on the Cottonwood course have won six of the last seven times.
Sharing fifth place with Dickerson at 3 under were Dean Wilson, Bo Van Pelt, J.J. Henry, Ryuji Imada, James Driscoll and Hunter Mahan on the Cottonwood course, and Nathan Green, Tim Herron and Omar Uresti at Las Colinas.
Ernie Els, competing at Las Colinas, leads a group of eight players knotted one stroke further back in 15th place.
Last week's winner at the Wachovia Championship, Jim Furyk opened with an even-par 70 at Cottonwood and is among a group of 16 players tied for 38th place.
Vijay Singh and defending champion Ted Purdy were also at even par after beginning their rounds at the Cottonwood course.