Kupcho patted her friend's shoulder when Fassi answered with a shot that rolled back to a foot for birdie on the next hole.
While the sight of women battling for a trophy was new for Augusta National so were the sounds as the galleries offered encouragement with shouts of "Atta girl" and "Way to go girls".
The top 30 players in the 72-strong field made the cut.
The American turned up the pressure another notch with a birdie at 16 as Fassi blinked taking a bogey, her first since the opening hole, to hand Kupcho a two shot advantage with two to play.
Augusta National announced its Women's Amateur previous year at the Masters, creating an opportunity for some of the best amateurs in the world to showcase their skills on a course where Jack Nicklaus, Arnold Palmer and Tiger Woods have created so many big moments.
In a dramatic battle between two 21-year-old United States collegiate stars, Kupcho had three birdies and an eagle in the last six holes in firing a five-under par 67 to finish 54 holes on 10-under 206 for a four-stroke victory over Fassi, who fired her third consecutive 70.
"I started out strong and was hitting the ball really well", Kupcho said.
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The first two rounds were played at the Champions Retreat course in Evans, Georgia.
But Kupcho, who made bogey at No. 10, drew even at the par-5 13th.
That was answered by a birdie from Fassi at the 14th as she holed a tricky downhill putt, but Kupcho hit back again with another superb second shot over the water at the par-five 15th to set up a birdie from the back of the green.
Earlier, on Friday, South Korea's Kim Si-woo fired a brilliant hole-in-one to surge into a four-shot lead at the Valero Texas Open in San Antonio. "I knew I was going to be able to do it".
That moment of magic helped turn a two-shot lead into a four-shot cushion, leaving Kim at 12 under with two to play.
Meanwhile, young Thai talent Sadom Kaewkanjana held his nerve on Saturday to become the fastest qualifying school graduate to win on the Asian Tour when he clinched the Bangabandhu Cup Golf Open by one shot. "So I think we'll make a lot of birdies, and it will be pretty fun to watch us".
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