Gauff, who is playing at a Grand Slam tournament for the first time, won 3-6, 7-6 (7), 7-5 on Centre Court.
Hercog's first match point came and went on Gauff's serve at 3-5, with a second arriving a game later when she was serving for the match.
Gauff maintained her momentum as she played near flawless tennis to break Hercog in the fourth game of the decider before showing signs of tension as she was broken comfortably three games later.
On the other side, eight-time Wimbledon Champion Roger Federer has also qualified to the second round of men's singles after defeating African player Lloyd Harris by 3-6, 6-1, 6-2, 6-2 at Centre Court.
In her very short professional career, Gauff had won just over $75,000 in prize money.
But Gauff climbed off the canvas and showed she has a strong fighting spirit to add to her precocious talent, earning a 3-6 7-6 (7) 7-5 victory over the Slovenian. Despite her nods to everyday teenage past-times, Gauff insists she has a serious streak.
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Gauff is the youngest player ever to qualify for Wimbledon.
"I think she s having obviously the time of her life playing at Wimbledon and Court 1 and beating Venus and all of these things, which is incredible". It was my first match on Centre.
That means Williams could have to play twice on Saturday (UKT), when she is supposed to face Julie Goerges in the third round of singles. I was focused the entire match and it was incredible.
The American will play the last match of the day at the All England Club's biggest stadium when she faces Polona Hercog of Slovenia, another unseeded player.
"There are a lot of factors that go into that, but I think as long as she stays happy and is able to continue to play well, I think she ll be fine".
Nerves perhaps got the better of her to begin with as for the best part of two sets she barely laid a glove on the world number 60.
The victor of this match will set up a tough tie against either 2018 French Open champion and seventh seed Simona Halep, or two time Australian Open champion and Wimbledon semi-finalist Victoria Azarenka.