The 18-year-old Suwon native needed two hours and 13 minutes to secure a victory that will make many take notice of the 2013 Wimbledon Junior Championship finalist.
"It was tough - the weather, the conditions and playing against a high-ranked player, everything was tough," said Chung.
"But I was motivated - I knew if I won that I would get an even better opportunity to play a better player."
The Korean, who wears glasses during matches due to a developmental eye disease, has risen to 121st in the world and his reward for his victory is a tough test against eighth seed Czech Tomas Berdych.
American Jack Sock, who reached the fourth round at Indian Wells last week before losing to Roger Federer, advanced with a 6-3 6-4 win over Japan's Go Soeda.
In an all-German clash, Jan-Lennard Struff saved three match points as he got past Benjamin Becker 3-6 7-6 (10) 6-4.
Australian qualifier James Duckworth defeated Bosnian Damir Dzumhur to earn a meeting with Spain's Fernando Verdasco.
Britain's Andy Murry will face American Donald Young after his opponent, Lu Yen-hsun of Taiwan retired in the first set due to a neck injury.
(Reporting by Simon Evans; Editing by Frank Pingue)
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