Duke and Tringale both shot seven-under 65 on the par-72 TPC Louisiana course.
Tringale surged to his share of the lead with birdies at the last four holes, recovering from his early bogey at the par-three third with eight birdies overall.
Duke, who like Tringale is seeking a first career US PGA Tour victory, had seven birdies, including three in a row from the fifth. He had two more at 11 and 12, and capped his round with a birdie at 18.
They were one stroke in front of South African Ernie Els, Sweden’s Daniel Chopra and Americans Steve Stricker and Chris Stroud.
Els made a birdie from a bunker at 18 to cap his 66. Stricker started on the 10th tee and after his only bogey of the day, at the par-five 18th, played his last nine holes in five-under.
It was another shot back to Ben Curtis, John Rollins and Jason Dufner on 67. Former British Open champion Curtis arrived in Louisiana fresh from victory in the Texas Open on Sunday, his first tour title since 2006.
Watson had four birdies and three bogeys in his 71. He admitted he was “mentally exhausted” in the wake of his first major title at Augusta National earlier this month.
He teed off on 10 and was two-over through seven holes. He held on, however, and finished his round with three bogeys and four birdies.
“Very happy with my score today,” Watson later said via Twitter. “To shoot under par was awesome!”
England’s Luke Donald, ranked second in the world, signed for a 73.
The announcement at COP28 in Dubai puts Turkey in the race against Australia