The 27-year-old del Potro is playing his third tournament since returning to the ATP Tour following left wrist surgeries. He is currently ranked 366th because of extended inactivity.
"I'm going to try to play my best tennis against Roger," Del Potro said. "We're both coming off injuries but I think it will be a really good match."
Del Potro won the first set in less than a half hour against the 39th-ranked Pella.
Del Potro let a match-point slip away with Pella serving at 4-5 of the second set, but completed the match in the tiebreaker.
"It was a tough moment for me but I got through and that's all that matters," Del Potro said.
Del Poro has already improved on his Miami Open performance of last year, when he lost his opening-round match to Vasek Pospisil in what was his final match of 2015.
Del Potro reached the semifinals in his first comeback event this year in the Delray Beach Open, and lost in the second round of the BNP Paribas Open last week.
The most significant result on the women's side was Lucie Hradecka's 6-4, 3-6, 6-2 victory over 2014 Wimbledon finalist Eugenie Bouchard.
Several American women also advanced. Irina Falconi of the United States defeated Francesca Schiavone of Italy 7-5, 6-1, American Vania King took out Lourdes Dominguez Lino of Spain 6-4, 6-4, and Christina McHale of the United States eliminated Misaki Doi of Japan 6-2, 4-6, 7-5.
McHale faces top-seeded Serena Williams on Thursday.