The current Asian champion, Su had to fight a painful knee injury as well as a fired-up Cheong, but came through to win 1-0 with a defensive kick in the third round of the women's under-57kg division.
The result ended Cheong's Olympic tournament, with a one-win, two-defeat record.
Her 1-0 win over Miriam Bah (Ivory Coast) was the first time a New Zealander had progressed past the first round in taekwondo since the sport joined the Olympics at the Sydney 2000 Games.
Cheong was forced into a tie-breaking sudden death fourth round before she scored the first -- and only -- point of the bout with an offensive kick.
The win earned her a quarterfinal match against world No 1 Sujeong Lim (Korea) later in the day.
Although Cheong started well, matching Lim in the early stages of the three-round bout, the Korean powered away with a flurry of telling blows in the closing minute of the final round for a 4-1 points win.
Cheong, 19, was left lamenting what might have been.
"I think I fought the first and second rounds OK, but the last round was a bit of a muck-up," she told NZPA.
"She's got way more experience than me and she stayed calm. I started running into her, so she knew me very well. I knew her too, but I guess I wasn't quite there."
Cheong, who was born in Korea and came to New Zealand when she was seven years old, has been studying taekwondo with coach Jin Keun Oh for 12 years.
She said she hoped Lim would go on to take the gold medal.
"I looked up to her when I was little, she's the one who motivated me to do taekwondo. Being in the same ring with her was great. And that's my home country, where I was born, so I'm happy that Korea won."
Cheong's teammate Logan Campbell took the mat in the men's under-68kg class against one of the strongest starters in the division, reigning world champion Yu-Chi Sung of Taiwan, who was making his Olympic debut.
Although Campbell broke his arm in a bout barely seven weeks ago, he wasn't about to let that stop him from giving 100 percent.
"We went over to Europe and did three competitions in a row," Campbell said.
"I fought a real tall guy from Senegal -- he kicked me in the arm and just snapped it."
Campbell said the left-arm break had healed quickly and caused him no problems in today's competition.
He started well in the three-round bout, keeping Sung scoreless until well into the second round. But Sung's superior speed and technique were always going to pressure the Aucklander, who conceded two points to trail 0-2 going into the final round.
Sung upped the tempo to score twice more in the final minutes for a 4-0 points win as Campbell's lack of international experience began to show.
Campbell, 22, was philosophical about the loss.
"It was a tough competition -- he's the current lightweight world champion. It was a hard draw straight off but if you want to be the champion, you've got to beat the champion. I just couldn't do it today."
Sung was later beaten by Taejin Son (Korea) in the semifinals, ending Campbell's hopes of making the bronze medal repechage.
