The Belgian, a three-time champion at Flushing Meadows, opened the first night session of the tournament against 16-year-old wild card Duval, the youngest player in the draw.
Clijsters announced earlier this year that the final grand slam of the year, and the venue where she has had the most success, would be her last event before retirement.
While the 29-year-old is very familiar with the vast arena that is Arthur Ashe Stadium, for Duval it was a daunting venue to make your grand slam debut.
The teenager, who spent much of her youth in Haiti, has already been through a lot in her life, including being held hostage by robbers in Port-au-Prince when she was seven.
Her doctor father, meanwhile, was injured in the Haitian earthquake in 2010 and was airlifted to Florida after members of Duval's training centre in Atlanta donated money.
The 16-year-old earned a wild card by winning the under-18 national championships and gave a good account of herself, particularly in the first set, but Clijsters was too powerful in the end.
The 23rd seed next faces 18-year-old Laura Robson from Great Britain, who saw off fellow teenager Samantha Crawford 6-3 7-6 (8/6).
Clijsters insisted the thought that it could be her last match on Arthur Ashe had not really crossed her mind.
She said: "I didn't really think about that. I was just excited to be out there and to have the opportunity to play in these kind of conditions, prime time.
"A night match, it's always a very special occasion. The energy when you step out on court also after the opening show, the stadium was almost full. So it was a lot of fun to go out there."
It was fitting symmetry that Clijsters should begin her final tennis journey against a player just starting out on hers and the Belgian asked for a picture with Duval after the match.
"She's a very nice girl," said Clijsters. "I think she has a good game to be out there. Obviously it's a very overwhelming situation to be in to start off.
"I think in the beginning she was definitely a little bit nervous. You kind of have to get a feel for it. All of us. Even (Roger) Federer.
"But overall I think once she settled down she was pretty happy with the way that she played. So that's good to know that she's pleased with the experience.
"I saw her afterwards. It was pretty funny. There was a lot of excitement. She had a friend in there who still plays juniors. So it was kind of fun to still see the youngsters."