The two Americans met in a high-quality encounter on Center Court, but it was Anisimova who outperformed, winning 6-7 (4-7), 6-2, 6-1.
“This is the most special day of my career,” Anisimova said after her win. “It is a great privilege to play on this court playing Coco.
“Winning is very special, especially in front of a full crowd, you guys were amazing.”
The 18-year-old Gauff had started better than the two and took the lead in the first set before Anisimova began to settle – it was the first time she had played a match on the main court at Wimbledon.
At the end of the set, the pair had to be separated by a tie break which Gauff managed to get the better of before the momentum quickly shifted the other way.
Gauff’s first serve began to disappoint her in the second set and gave her opponent all the opportunity she needed to force a decider.
Anisimova, ranked 25th in the world, did not take her foot off the gas and continued to dominate from the baseline while reducing unforced errors.
The 20-year-old only got better as the match went on and was able to pull the match out with ease to advance to the next round, where she will face Harmony Tan on Monday.
“There are so many American players who are doing well and I am proud of my country and how we have done,” Anisimova added.
“It was really exciting to have a clash of Americans on this court, so it was really special.”