Del Potro, a Shanghai semifinalist in 2013, struggled with his second serve. Although he won 40 of 49 points on his first serve, he only captured 13 of 30 second-serve points.
American qualifier Frances Tiafoe advanced to the second round by beating Benoit Paire 6-4, 6-4. The 92nd-ranked Tiafoe was playing in his first main-draw match since a five-set loss to Roger Federer at the US Open.
"I hope I play Sam, two Americans, so their will be an American in the third round," Tiafoe said.
Chung Hyeon also advanced, defeating ninth-seeded Roberto Bautista Agut 6-4, 6-3. Chung saved all four break points he faced against last year's finalist.
"Today, I was trying to stay calm all the time in the match," said Chung, who only won one game when he played Bautista Agut in Dubai in 2016. "I won today so I did everything good."
Federer, who won the title in Shanghai in 2004, will play his opening match on Wednesday. The Australian Open and Wimbledon champion hasn't played at an official tournament since losing in the US Open quarterfinals.
"I'm playing just the big tournaments now," Federer said. "I've been practicing for hours on the Centre Court. I'm here for a reason. I'm here for a purpose. Hopefully to do well and winning the tournament.