Roger-Vasselin set up triple match point with a crosscourt backhand then wrapped up the match in one hour, 28 minutes when Del Potro's forehand return was long.
"I didn't play my best tennis today," said No. 1-seeded Del Potro. "I wasn't feeling 100 percent and the other guy played a great game."
Roger-Vasselin, ranked 189th, had nine aces against the fifth-ranked Argentine's six.
"It's unbelievable," Roger-Vasselin said. "I didn't expect this. It was tough in the first two games and then I saw that he wasn't playing that well and thought why not today?"
Del Potro reached the final of last year's Japan Open but clearly struggled with his game in Tuesday's match.
"I felt so happy after the U.S. Open," Del Potro said. "We had a good celebration with family and friends in Argentina, but I am disappointed about today's result. I have to keep improving."
Roger-Vasselin said he benefited from the first meeting between the two players.
"I'm sure I knew him much better than he knew me," said Roger-Vasselin. "This was a great match for me and obviously, not so good for him."
In another first round match, Australian Lleyton Hewitt defeated Japan's Tatsuma Ito 6-1, 7-5.
Top-ranked Roger Federer pulled out of the $1.2 million event, citing fatigue, along with third-ranked Andy Murray of Britain who withdrew because of a wrist injury.
Defending champion Tomas Berdych of the Czech Republic was to play later Tuesday against Japan's Go Soeda.