Anisimova quickly found herself 3-1 down in the first set but clawed her way back, trailing 5-4 before world number three Pegula fired off a love hold to win the set in 34 minutes.
Anisimova began the second set with more confidence and control, winning her first break point in the second game and quickly establishing a 3-0 lead before Pegula took a medical timeout, resulting in a short delay to the match.
Pegula returned to the court and was swiftly broken before taking the next two games. Although ninth seed Anisimova broke Pegula to win the set, her control appeared to be faltering heading into the decider.
Momentum started to swing Pegula's way as she won three straight games to open the third set, breaking twice.
Anisimova regained her composure and refused to fade away, erasing a 5-3 deficit to lead 6-5 before Pegula brought the set level and dug deep to win the tiebreak.
Anisimova showed great fight throughout the match but ended the day with 56 unforced errors.
In the semis, Pegula faces either seventh-seeded Iga Swiatek or second seed Elena Rybakina, who are scheduled to play later on Thursday.
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