Plagued by a serious wrist injury that handicapped him since his rousing five-set win over Roger Federer in the 2009 U.S. Open final, del Potro returned to form at the Rio Olympics, where he reached the finals before falling to Andy Murray.
The 6-foot-6 (1.98 m) Argentine backed up his impressive Rio run by rifling in 11 aces in eliminating Schwartzman, claiming the third-set tiebreaker 7-3.
"I am so glad to be part of this tournament once again after three years," said del Potro, who was given a wild card to join the main draw and said he was lifted by the crowd support.
"Always, in every match here at the U.S. Open, the crowd make me feels special. I really like the atmosphere down there."
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Del Potro said he was still feeling the effects of his efforts in Rio, where he ousted world number one Novak Djokovic in the first round and number five Rafa Nadal in the semi-finals before losing to second-ranked Murray in four sets in the final.
"To be honest, I'm still feeling tired," said del Potro.
"It's not easy after a big, big challenge like I did in Rio. But this tournament is very special for me. I'm trying to keep calm, to keep focussed, and look forward to go far.
"The people in Argentina, in my hometown, they know what (I) have been through to get there after my surgeries. It was a special moment for me. They really appreciate what I did to come back on tennis. They are proud to see me playing tennis again."
Del Potro said he was close to quitting the game.
"After the first surgery, the second one, and in the end the third one, it was really, really sad moments for me," he said. "Nobody knows what should I have to fix my problem.
"My family and friends help me a lot to never give up. And I think I'm doing well now. The worst part of my life is totally in the past, and I'm living a good present and looking forward for a good future."
Next up for del Potro will be 19th-seeded American Steve Johnson, who overcame Russian Evgeny Donskoy 4-6 1-6 7-6(2) 6-3 6-3 to advance.
(Editing by Steve Keating.)
