The 12-year-old, home-schooled seventh-grader from Coral Springs, Fla., also the youngest qualifier in U.S. Women's Open history and the recent Junior PGA champion, beat 12-year-old Pearl Jin 5 and 4 in a second-round showdown Thursday at Crooked Stick Golf Club.
Thompson came back later in the afternoon with another 5 and 4 win over 18-year-old Lizette Salas of Azusa, Calif., to reach Friday's quarterfinals against Korea's Ha Na Jang.
Thompson, whose father, Scott, is her caddy, didn't have a bogey in either round Thursday and stretched her streak to 33 holes over three rounds at par or better on the 6,595-yard course.
'I'm really happy with the way I'm hitting it,' she said. 'I'm just going in (Friday) and try to play the way I did today.
'This course is pretty long, especially when it's windy. I'm just really happy I made it this far,' Thompson said
Thompson and Jin were the first 12-year-old players to reach match play in the Women's Amateur.
'It's a great experience,' Jin, of San Gabriel, Calif., said of the preteen matchup. 'My swing was off. I didn't hit the ball solid, and my putts just didn't go in. I was nervous. It affected my swing and my putting, rhythm and tempo.'
Jang advanced to the quarterfinals with a victory over UCLA junior Tiffany Joh in 20 holes.
Another quarterfinal on Friday will match teammates Amanda Blumenherst and Jenny Lee of NCAA champion Duke against each other. Both had easy matches Thursday, with Blumenherst beating Marci Turner of Tompkinsville, Ky., and Lee downing Sara-Maude Juneau of Canada, both 6 and 5.
'I'm going to treat it like any other match,' Blumenherst said of her quarterfinal match against her friend and teammate. 'Obviously, we've played each other, three times a week all year. But it doesn't matter who I play. I'm just going to be playing my game.
'I have so many friends in this championship, so it's just a part of it.'
Among other third-round matches, Mina Harigae of Monterey, Calif., who won the U.S. Women's Amateur Public Links championship in June, beat Vicky Hurst of Melbourne, Fla., 1-up. Harigae advanced to the quarterfinals against Maria Jose Uribe of Colombia, who beat Emma Jandel of Dayton, Ohio, 2-up.