The 20-year-old needed four match points to eke out a 7-6 (6), 4-6, 7-5 win - his first in three FedEx ATP Head2Head meetings with the Argentine.
Eighth seed Chung overcame Croatia's Franko Skugor in straight sets 6-4, 7-6 to reach the last eight of the competition.
Hyeon Chung will meet fellow rookie Frances Tiafoe in the quarter-finals of the Delray Beach Open after the latter pulled off a shock win in Florida. World number 10 del Potro appeared to be on his way when he seized an early 3-0 lead, but he was unable to capitalize on four set points as he dropped the opener in the tiebreaker. The tight third set saw del Potro save a match point against in the 10th game, and two more in the 12th before Tiafoe gained just the second win against a top-10 player in his career.
But Tiafoe produced a performance beyond his years to reach the quarter-finals, firing down 17 aces and saving 14 of 16 break points as he thwarted the 2009 US Open champion.
Isner noted after his win yesterday that the lack of match play made it tough for him to get his footwork going, but winning real matches would help. "He made three straight first serves, and he hit a insane, high, backhand drop shot, angle thing on the first match point, which was a good shot". "Just wanted to get over the line".
Hard-hitting Canadian Denis Shapovalov also advanced with a 6-7 (6-8) 6-4 6-4 win over Jared Donaldson.
"I definitely picked up my serve in the second and third set", Shapovalov said.
While Lincoln native Jack Sock went the academy route as a tennis player, living and training full-time in Kansas City as a junior, Jackson Withrow stayed in Omaha and became a three-time state champion at Omaha Burke. "I think both of us were playing well".