Leishman opened with a 61 in Trinity Forest's debut, after the Nelson spent 35 years at the TPC Four Seasons.
The wind didn't bother Wise, who shot a bogey-free 63 in the afternoon.
Wise said the difference with strong wind on the course co-designed by Ben Crenshaw showed up quickly when his tee shot on the par-3 second hole ended up 30 yards right of his target.
"My speed has been really great", he told the Golf Channel. "Especially around here because there are no trees out there, nothing to really block it".
The forecast Saturday has wind gusts reaching 25 miles per hour, and the player with the highest world ranking in the field at No. 3 is hoping for at least that. However, Spieth said he was more comfortable on the greens overall in the second round. "I made an adjustment that I had been talking about making. Wish I got more out of it, honestly". He cooled off with three bogeys and two birdies coming in to card a 66.
Wise, who tied for second in the Wells Fargo Championship two weeks ago, said he used the Australian as an incentive.
"I think best said under the lesson if you don't have anything nice to say, don't say anything at all", he said. "Last week at The Players I hit a lot of really good putts that lipped out, and this week they're going in".
"It makes this course play way different just because of how firm and fast it is", Wise said. "Firming up a bit, but the weather was lovely, wasn't a lot of wind". "It's going to start to change significantly on the weekend".
Want to feel better about that gimme putt you totally blew on the course the other day? "On the back nine today you could kind of anticipate some bigger roars as the putts were about to go in".
A further two shots back is Billy Horschel, the defending champion, who shot a 69.
However, it was not quite enough to achieve his goal of a climbing into the world's top 60 to secure a start in next month's US Open and extend his run of 67 consecutive majors played.
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