The pair were delayed from taking the court on Thursday because of more rain and then had to endure another weather-related suspension just six minutes into their match.
Del Potro was not rattled by the delays and did well to attack Chung’s forehand throughout the 81-minute encounter that determined the final entry into the last 16.
This marks Del Potro’s fourth consecutive last-16 appearance in Cincinnati, where the Argentine appears to be in fine form right in time for the US Open.
Next up for Del Potro, who this week reached a career-high third in the world rankings, will be a clash with Australian 15th seed Nick Kyrgios.
In third-round action, big-serving Milos Raonic beat fellow Canadian Denis Shapovalov 7-6 6-4, while Spanish 13th seed Pablo Carreno Busta topped Dutchman Robin Haase 6-4 6-2.
Rain then halted the third-round action, including a scheduled match between seven-time champion Roger Federer and Argentine Leonardo Mayer which will now take place on Friday.
Novak Djokovic was leading Grigor Dimitrov 2-6 6-3 2-1 when their match was suspended. The winner of that contest will face Raonic in the last eight, while Carreno Busta will take on either Marin Cilic or Karen Khachanov who were into a deciding set before the weather intervened.
Stan Wawrinka’s encounter with Marton Fucsovics was also suspended.
Watch the Cincinnati Masters resume on Sky Sports Arena at 6pm on Friday.