The pair began the final round three shots back and closed with a seven-under 65 in alternate-shot play to finish with a tournament-record total of 30-under 258 at TPC Louisiana, eclipsing the 259 posted by 2022 winners Patrick Cantlay and Xander Schauffele.
Hardy and Riley won by two shots from Canadians Adam Hadwin and Nick Taylor.
Riley's previous best finish was a playoff loss to Sam Burns in the 2022 Valspar Championship. Hardy's best was a tie for fifth at the Sanderson Farms Championship last fall.
Each takes home $US1.24 million and earns a two-year exemption for winning the PGA Tour's only team event.
"It was nerve-wracking, honestly," Riley said. "The first win is always tough.
"You're just rooting for each other as hard as you can to hit a good shot," Riley added. "Luckily we were able to do that. ... I was pretty nervous coming down the stretch."
Hadwin and Taylor shot 63, tying the course record in alternate shot that was set in Friday's second round by Cantlay and Schauffele.
The Canadians' 10th and final birdie of the round on the 13th hole briefly gave them a one-shot lead, and they went to the clubhouse tied for first before the eventual champions birdied twice more.
Wyndham Clark and Beau Hossler, who finished each of the first three rounds atop the leaderboard and opened the final round with a one-stroke lead, made their first three bogeys of the tournament - two on their final three holes - and closed with a one-under 71 to finish third, three shots back.
Cantlay and Schuffele made eight birdies before their second bogey of the day on 18 left them tied for fourth with Matthew NeSmith and Taylor Moore at 26-under.
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