The two Americans met in a quality match on Center Court, but Anisimova performed the best, winning 6-7 (4-7) 6-2 6-1.
“This is the most special day of my career,” Anisimova said after the victory. “It is a huge privilege to play on this court as Coco.
“Winning is something special, especially in front of a full crowd – you guys were amazing.”
Gauff, 18, started the better of the two and took the lead in the first set before Anisimova began to adjust – it was the first time she had played a match on Wimbledon’s main court.
By the end of the set, the pair had to be split in a tiebreak, which Gauff managed to manage before the momentum quickly changed.
Gauff’s first serve started to let her down in the second set, and it gave her opponent all the opportunities she needed to force the deciding set.
World No. 25 Anisimova didn’t take her foot off the gas and continued to dominate from the backline, cutting back on unforced errors.
As the match went on, the 20-year-old only got better and was able to play the match with ease to advance to the next round, where she will face Harmony Tan on Monday.
“Many American players are doing well, and I am proud of my country and our success,” Anisimova added.
“It was very exciting to have an All-American clash on this court, so it was really special.”