Seven Britons had failed to progress beyond the first round heading into the 19-year-old's match, which she took 6-3 6-4 on Court One.
The home hope won the girls' title on the same court five years ago and will now face Colombia's Mariana Duque-Marino.
"I am still so nervous, even on the last point I didn't know whether my forehand was good or not," she told the BBC.
"I think that was a big one for me because of all the nerves and playing in front of your home crowd at Wimbledon. It is a big one.
"I could have gone 5-1 up in the second and lost my focus a little bit. I started to think about winning and I got back to focusing point by point. I thought I served pretty well today [Tuesday].
"[Winning silver at the Olympics in the mixed doubles] definitely boosted my confidence. Any big win gives you loads of confidence so I am going to go into the next match with a good focus, I think."
Serena Williams was able to turn her attention to on-court matters on Tuesday as she won the first match of her Wimbledon defence with consummate ease against Mandy Minella.
A five-time champion at the All England Club, the American dominated from the outset and romped to a 6-1 6-3 victory in 57 minutes.
Agnieszka Radwanska bounded through to the Wimbledon second round as the Polish player who reached last year's final dropped just two games in her opener.
Radwanska, 24, who fell ill on the eve of last year's final before pushing Serena Williams to three sets in the title match, was able to ease past Austrian Yvonne Meusberger on Court Two.
Seeded fourth, and a quarter-finalist at the Australian Open and French Open this year, she will hope for another long run in London and a 6-1 6-1 victory set her on the way.
Radwanska, who fired down five aces, faces Mathilde Johansson of France in the second round.
Williams now faces a second round tie against France's Caroline Garcia, who beat Jie Zheng 6-3 6-4 on Tuesday afternoon.
Sixth seed Li Na secured safe progression to the second round after beating Michaella Krajicek 6-1 6-1, while 11th seed Roberta Vinci won to set-up a clash with Jana Cepelova.
Alexandra Cadantu overcame 28th seed Tamira Paszek and will now face Kimiko Date-Krumm, who, aged 42 and 270 days, defied her years once again as she took just 44 minutes to beat Carina Witthoeft.
At the other end of the scale, 18-year-old American Madison Keys defeated home favourite Heather Watson 6-3 7-5.
The major casualty was world number 10 Maria Kirilenko after losing 6-3 6-4 to home favourite Laura Robson, who will play Colombia's Duque-Marino next.
2011 US Open champion Samantha Stosur eased past Anna Schmiedlova, while there were also wins on Tuesday for Olga Puchkova, Mona Barthel and Simona Halep.
Marina Erakovic faces Shuai Peng in the second round after both secured wins on Tuesday afternoon, while Romania's Simona Halep is also through.