Watney, the 25-year-old Californian in his third year on the tour, had a 15-under 273 total at the TPC Louisiana. Duke, who also was seeking his first victory, shot a 70.
"I'm living a dream right now," Watney said, wearing Mardi Gras beads as winners in New Orleans traditionally do. "I've played in close to the last group sometimes, and I've seen guys go through it. But it's definitely more fun to actually do it. I'm trying to soak it all in."
Watney, fifth in two tournaments last year, lost the lead when he missed a 3-foot par putt on the par-4 10th. He bounced back with a birdie on the par-5 11th and went in front for good with a birdie on the par-3 14th.
On the 14th, Duke's tee shot landed short and left of the green, his chip went 7 feet past the pin and he missed the par putt coming back to fall two shots behind.
Watney parred the final four holes, missing the fairway only once off the tee and hitting every green in regulation.
"I knew if I could get it to one coming to 18, I thought I had a chance, but he had two on me, and he played smart, and that's what you've got to do," Duke said.
After Watney tapped in to seal the victory, his celebration was subdued. He held aloft both arms and hugged his caddie before clapping above his head in appreciation of the crowd.
Watney had never before teed off with the lead in the final round of a PGA Tour event, and he hadn't slept as well as he usually does, waking up around 5:30 a.m.
He bogeyed Nos. 3 and 4, but then holed the shot of the tournament - a 132-yard approach shot for an eagle on the par-4 fifth - to pull back into a tie for the lead.
"I was definitely nervous to start out, but it's a good thing," Watney said. "I mean, anytime you hole a shot there's a little luck involved, so it was definitely my week. I'm proud that I was able to handle it."
Watney became the fifth first-time winner in the past six years at New Orleans' annual PGA Tour event, joining Chris Couch (2006), Tim Petrovic (2005), Steve Flesch (2003) and K.J. Choi (2002). All of them won at English Turn except Watney and Petrovic, the only other winner at the TPC Louisiana - which hosted its first PGA Tour event in 2005, only months before it was severely damage by Hurricane Katrina.
The course, its fairways flooded because of drain clogging debris that included 2,000 fallen trees, was closed for 10 months for $2 million in repairs to 30 acres of damaged turf.
But New Orleans seems to be kind to players who've never won, regardless of the course, in part because some the tours top players often skip it.
Heading into the final round, 13-time winner Mark Calcavecchia was the only player in the top five with a previous victory. He started the day only three shots back, and appeared primed to close in on the lead when his second shot on the par-5 seventh hole landed just off the fringe. He botched his chip, however, leaving himself a 35-foot birdie putt that he narrowly missed.
While the other players in his group putted out, Calcavecchia stood on the front edge of the green, staring back at the seventh fairway and shaking his head.
He missed another birdie putt on No. 8 and two bogeys on the back nine put him out of contention. He shot a 71 to tie for fifth with Bubba Watson and Chris Stroud at 10 under.
Tour rookie Anthony Kim had the best round of the day, a 65 - one shot off the course record that fellow rookie Kyle Reifers set Thursday. The round of nine birdies and two bogeys left the 21-year- old Californian tied for third with John Mallinger at 11 under.
"I was so far back I really didn't have anything to lose, and I just fired at some pins and it worked out," Kim said. "My goal is to win out here, and until I do that, I'm just going to keep plugging away."
DIVOTS: Reifers, who led after the first round and began the final round only four shots back, shot a 75 to tie for 24th. ... Officials estimated the final-round crowd at about 40,000. Recent tournaments, including the last one prior to Hurricane Katrina in the spring of 2005, were closer to 35,000.