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, 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 her first meeting with 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.
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