Jordan Spieth - still searching for his first win of the year - managed a five-under 66 to move into seven under, enough to leave him tied for 20th.
Leishman teed off on 10 and kick-started his round with a 56-foot birdie putt at the par-three 12th. Every other time I've been close I had thought about it, but today with the greens as penalizing as they are if you hit a bad shot, you have to be so on.
May 17, 2018; Dallas, TX, USA; Aaron Wise acknowledges the gallery after making a birdie on the 18th hole during the first round of the AT&T Byron Nelson golf tournament at Trinity Forest Golf Club.
"First time I've been in the hunt with something to look back to", said Wise, who charged late but came up short at the Wells Fargo this month. "I know better than that on certain shots".More news: The Royal Wedding: Prince Harry, Meghan Markle, And The Guests
Leishman broke the 36-hole record of 12-under 128 achieved on six prior occasions at the tournament's former home of TPC Four Seasons, including twice by Tiger Woods and most recently by Jason Kokrak a year ago.
Wind gusted above 25 mph at times after two rounds of calmer conditions and lower scores on the treeless, links-style layout a few miles south of downtown Dallas.
QUOTABLE: "I didn't even think about 59".
Leishman said there was a big difference in him shooting a four-over 76 in the final round of last week's Players Championship and his play in Dallas. "It's knowing what I shouldn't do and it's just me trying to get greedy".
And all too familiar for Spieth in front of the home folks.More news: TX school shooting victims: Pakistani exchange student, junior art student among victims
"I just pulled it and so obviously really frustrated, I missed two putts, one inside a foot, one inside of three feet with all the progress I made in my putting".
"It makes this course play way different just because of how firm and fast it is", Wise said.
"It was about as easy tee to green as I've ever seen this place", Spieth said. "I'm excited there's wind". "I like how the ball is running out in the fairways".
Leishman, who still has a chance to be a wire-to-wire Nelson victor two years after Sergio Garcia did it, retook the lead with birdies at Nos. "I played very well over there".More news: How Karnataka Dalit, Lingayat cards didn't work for Congress