"I was super calm. I was more nervous yesterday oddly enough," Wise said in a greenside interview at Trinity Forest in Dallas.
Two weeks after finishing equal second in Charlotte, Wise started the final round tied with Leishman but notched six birdies in a seven-hole stretch from the fourth in front of a gallery including former U.S. president George W. Bush.
He was never challenged thereafter and finished at 23-under 261, well clear of Australian Leishman whose final-round 68 was only good enough for second place on 20-under.
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PGA Tour rookie Wise, who moved with his parents to the U.S. at the age of three, had an outstanding amateur career and won the American collegiate championship in 2016 before turning pro.
He said his runner-up finish in Charlotte had boosted his self belief and helped him deal with the pressure down the stretch on Sunday.
"I felt oddly calm all day long and to pull that off and play as good as I did, bogey free, was awesome," Wise said.
He is the first 21-year-old to win on tour since Kim Si-woo at last May's Players Championship.
Wise's performance certainly impressed six-times major champion Nick Faldo, who offered up some free advice.
"With a swing like that, don't mess with it," Faldo said during the CBS coverage.
Scores on Sunday were low after heavy morning rain took the fire out of the course and delayed the start of play by four hours.
South African Branden Grace took full advantage of the conditions to match his career-low round of 62 on his 30th birthday.
"To come in with nine under is pretty special, a great birthday present," said Grace, who tied for third on 19-under.
Grace made history at the British Open at Royal Birkdale last year when he became the first player to shoot 62 in a major championship.
(Reporting by Andrew Both in Cary, North Carolina, editing by Nick Mulvenney)
