Six-time Grand Slam champion Djokovic who captured his fourth Australian Open crown in January, launched his quest for a fourth consecutive US Open final by beating Lithuanian 112th-ranked Ricardas Berankis 6-1, 6-2, 6-2.
"I managed to make a lot of breaks in the beginning of the match and take over control," Djokovic said. "That's what I wanted to do. I wanted to play every point like it's match point and I'm happy with the performance overall."
Djokovic fired 10 aces and 28 winners and needed only 82 minutes to put himself into a last-64 matchup against Germany's Benjamin Becker.
Djokovic, the 2011 US Open winner who lost to Andy Murray in last year's final and last month's Wimbledon final, improved to 12-1 in Arthur Ashe Stadium night matches, what he called "the most special night matches of any tournament anywhere in the world."
Duval, a daughter of Haitian parents ranked 296th in the world, pulled the day's shocker with a 5-7, 6-4, 6-4 victory over Australian 11th seed Stosur in a tense struggle that lasted for two hours and 39 minutes.
It was only the second Slam match for Duval, who lost to Kim Clijsters last year at New York, and was her first match against a top-20 rival.
Stosur made 56 unforced errors, 21 more than Duval, on her way to a her 15th first-round Slam exit, the first since last year's Australian Open.
"Just let every single opportunity slip away and made too many errors and it really cost me," Stosur said. "I needed to step up more and do more. I'm not going to be a sore loser and say she didn't do anything but I certainly helped her out there, that's for sure."
Stosur split with long-time coach David Taylor just ahead of the US Open, but said she could not say if that was a factor in the loss.
"I don't know. Who knows?" she said. "It is what it is. I can't change it. I made the decision I made at the time and I stick by it."
"There wasn't much rhythm out there, but I was happy the way I played," said Federer. "Overall I'm pleased to be in the next round."
The 32-year-old Swiss star, who as the seventh seed is at his lowest spot in the US Open since 2002, will face Argentina's Carlos Berlocq in round two.
Federer, whose 56th Grand Slam start in a row matched South African Wayne Ferreira for the all-time record run, has only one title in his past 14 Slam starts, that coming last year at Wimbledon.
After a second-round exit this year at Wimbledon, Federer took only 93 minutes to eliminate Zemlja despite surrendering a third-set break.
"You're going to have sonme hiccups like I had today. It was a minor one," Federer said. "I might have had more confidence if I had closed it out without that. This way I had to fight a bit more. Who knows? Maybe that gives me confidence too."
Federer, who won five US Open titles in a row from 2004-2008, has not made the championship match on the Flushing Meadows hardcourts since losing to Juan Martin Del Potro in the 2009 final.
This year, Federer is on a quarter-final collision course with second seed Rafael Nadal, whom he has never faced at the US Open.
Two-time Australian Open winner Victoria Azarenka, who lost to Serena Williams in last year's final, downed German Dinah Pfizenmaier 6-0, 6-0. The second seed from Belarus faces Canada's Aleksandra Wozniak next.
"Last time I was here it was very emotional. I'm happy to be back," said Azarenka.
"I raised my level when I needed to. There were a few unforced errors (10) but overall I felt pretty consistent."
Canadian 10th seed Milos Raonic fired 28 aces in defeating Italy's Thomas Fabbiano 6-3, 7-6 (8/6), 6-3, while fellow big server John Isner blasted 16 aces to down Italy's Filippo Volandri 6-0, 6-2, 6-3.
Raonic, 22, is confident his first Slam quarter-final is within reach.
"I think I can put myself in that position," Raonic said. "I just have to make the opportunities and convert them. If I play well, I can get very close if not do it. I think I can get much better."
Czech seventh seed Petra Kvitova, the 2011 Wimbledon winner, outlasted Japan's 92nd-ranked Misaki Doi 6-2, 3-6, 6-1, while Danish sixth seed Caroline Wozniacki, the 2009 US Open runner-up, dispatched 133rd-ranked Chinese qualifier Duan Ying-Ying 6-2, 7-5.
US Open: Roger Federer, Novak Djokovic, Victoria Azarenka cruise into Round 2
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