Andreeva, who came through qualifying and is playing her first senior grass-court tournament, defeated 22nd-seeded compatriot Anastasia Potapova (22) 6-2, 7-5.
The key part of the match came when she had to fight back from 1-4 down to 4-4 in the second set.
She then saw seven break points come and go in the ninth game before she gathered herself to reel off the next three games for victory.
She credited her fighting spirit to Nadal, a 22-time major winner and celebrated chaser of lost causes.
"I was really impressed when Rafa came back after an injury, he won the Australian Open in 2022, he won French Open," she explained.
"I can say that mental-wise I just try sometimes to copy him. I try to remember what would he do in these moments, what would he do on the score."
Andreeva arrived at Wimbledon having made a run to the third round at the French Open, also out of qualifying.
She will now rise in the rankings from 102 to the top 65 at least after Wimbledon.
At the end of 2022, she was down at 293 before announcing herself on the WTA Tour with a run to the last 16 in Madrid in April.
When she started that tournament she was still 15.
NORMAL TEEN
Despite rocketing to fame, Andreeva insists she is just a normal teenager despite the riches her successes have produced.
At the start of 2023, her career earnings stood at just under $27,000.
Now, her bank balance has comfortably burst through the $500,000 barrier.
"I love to watch some series," said Andreeva of her life off the court. "I have to do my school. I have no choice. I have to suffer for two more years, and that's it.
"I'm still 16, and sometimes I can be like a kid. I can complain a lot about some stuff."
She added: "When I have free time, sometimes I prefer to be alone, just with myself. But most of the time I watch Netflix."
As well as winning over fans at the All England Club, Sunday's win came on the birthday of her grandfather, watching on TV at the family home in Krasnoyarsk, Siberia.
"I feel the support from Krasnoyarsk, a lot of people are posting the stories," said Andreeva.
"They are tagging me everywhere. I feel super nice because they remember me. I'm excited about it, that they still cheer for me, even though I've been there last time in the winter."
On Sunday, Andreeva made the most of Potapova's mistake-ridden performance.
When Potapova buried an overhead into the net on match point it was her 45th and final unforced error.
"It was an amazing battle," said Andreeva.
She refuses to compare her run to that of Britain's Emma Raducanu, who captured the 2021 US Open title after coming through the qualifying round.
"She did an amazing job to pass the quallies and to win the Slam at 18.
"But me, I try to not think about it. I think it will disturb me, all these thoughts."
Despite her breakthrough performance, Andreeva maintains loftier ambitions and is targeting the seeded players' dressing room at Wimbledon in 2024.
"I hope to be in the locker room above next year," said the teenager, who will face US 25th seed Madison Keys on Monday for a place in the quarter-finals.
