The Frenchwoman wasted no time in putting pressure on Gauff, stepping into the court to attack her second serve and clobbering forehands to race out to a 4-0 lead as rain-soaked fans were still finding their seats at Arthur Ashe Stadium.
Garcia, seeded 17th, took the first set with an exquisite volley and kept her foot on the gas in the second, breaking Gauff in the first game to keep the New York crowd hushed.
Gauff, the 12th seed, had her best chance of climbing back into the match when she had a breakpoint opportunity to get back on serve while trailing 3-2.
But Garcia fired two unreturnable first serves and held after an exhausting rally when Gauff's passing shot sailed long, leaving the teenager looking dejected.
Garcia sealed the win when Gauff's backhand landed in the net on match point, stretching out her arms and racing around the court to celebrate reaching her first Grand Slam semi-final.
"The atmosphere was very strong obviously to play an American here, it's like crazy energy," Garcia said on court.
"My head is just buzzing."
Since coming back from a foot injury in May, Garcia has won three events on three different surfaces - on clay in Warsaw, where she beat world number one Iga Swiatek, grass in Bad Homburg, and the hard courts at the Cincinnati Open.
Garcia has yet to drop a set at this year's US Open and Tuesday's win was her sixth straight over a top-20 player and first against Gauff in three career meetings.
"I have always played very aggressive and the last couple months I felt antsy again so I'm able to move and practice the way I want," she said.
"I just go for my shots even when I'm stressed or even when I don't feel it. The way to improve for me is to move forward and I just try to follow that way."
US tennis fans eager to see a player fill the void left by the outgoing Williams have pinned their hopes on Gauff and while she may not be ready yet, her quarter-final run guarantees she will enter the top 10 for the first time after the tournament.
There were mixed feelings for the young American after the match.
"Overall I'm super proud of myself in this tournament," Gauff told reporters.
"But I'm hungry for more. So maybe next year."
Gauff said she had been a bit hesitant coming into the tournament after rolling her left ankle and retiring from a tune-up event in Cincinnati last month.
"I'm just proud of how I was able to come through this week. After everything that happened in Cincinnati, I didn't tell anyone, but I didn't think it was going to be that good of a tournament for me," she added.
"I really proved to myself mentally that I can come out of these tough situations and do it.
"First quarter-final, too, at the US Open, so there's a lot to be proud of. But, like I said, definitely disappointed. I think it makes me want to work even harder. I feel like I know what I have to do."
Gauff also said she hopes she can be an example for the next generation of Black players like Serena and Venus Williams had been for her.
"The Williams sisters definitely inspired me to play tennis because I saw someone like me playing in a sport with not a lot of people looking like me," she said.
"I hope I can be that for other kids."
Next up for Garcia is a semi-final against Tunisian fifth seed Ons Jabeur.
"Since juniors she has been a big player and a tough one for me so I'm looking forward to the next challenge and seeing what I can improve," she said.
