The American star recovered from a slow start to defeat Andreeva 2-6, 7-6 (7), 6-2 in a dramatic quarter-final that lasted more than two hours.
Andreeva appeared in control after taking the opening set, but Gauff refused to let the match slip away. The 21-year-old fought through a tense second-set tiebreak, saving two match points before eventually winning the set and forcing a decider.
Gauff then took control in the third set, breaking Andreeva's resistance to complete another comeback victory.
The result also strengthened Gauff's dominance over the Russian teenager. She has now won all six of their meetings on the WTA Tour, with three of those victories coming after she had lost the opening set.
The victory also extended Gauff's impressive winning streak to 11 matches. She arrived at Flushing Meadows in strong form after claiming the Cincinnati Open title before the US Open.
Gauff will now face second seed Elena Rybakina in the semi-finals. Rybakina secured her place in the last four by defeating Zheng Qinwen 3-6, 6-1, 6-4 in a contest that lasted two hours and 14 minutes.
Rybakina is also set to become the new world No. 1 on Monday, adding further significance to their upcoming clash.
Gauff and Rybakina have met twice previously, with both players recording one victory apiece. Their semi-final will therefore provide a decisive chapter in their developing rivalry.
The American's latest victory also underlined her impressive record at the US Open. She has now won 25 of her 31 matches at the tournament and remains in contention for a second title in New York after lifting the trophy in 2023.
The run marks Gauff's seventh Grand Slam semi-final appearance. According to Opta, only Venus Williams, with 12, and Serena Williams, with 10, have reached more Grand Slam semi-finals before turning 23 among active players.
Gauff has also reached the semi-finals at consecutive Grand Slam tournaments for the second time in her career. Her previous run came across the 2023 US Open, where she won the title, and the 2024 French Open.
