Thompson, of Sewickley, Pa., won both matches 4 and 3 as she increased her match-play winning streak in the Senior Amateur to 27 matches.
She won her third-round match over Bernice Gallagher of Cincinnati with 14 pars and one birdie. In the morning at the Barton Creek Resort and Club, Thompson beat Lynn Larson of Aurora, Colo., with 11 pars and a birdie.
'I got up early against both opponents today and was just playing for pars,' Thompson said. 'I'm happy to be in the quarterfinals, but I still have to play old man par to win.'
Only one other person has won five consecutive USGA titles. Carolyn Cudone won the Women's Senior Amateur from 1968-72.
Thompson, who has not trailed this year and hasn't even been taken to the 17th hole, will play second-seeded Anne Carr on Wednesday in a quarterfinal. Carr, of Seattle, beat Toni Wiesner of Fort Worth, Texas, 2 and 1 in the third round.
Medalist Sherry Bowman of Manassas, Va., lost 6 and 5 to Pat Milton of Munroe Falls, Ohio, in the third round.
'I just totally ran out of gas, I didn't have anything left to give,' Bowman said.
Fourth-seeded Cecilia Mourgue-D'Algue of France lost 3 and 2 to Patty Moore of Charlotte, N.C., in the second round.
Carolyn Creekmore of Dallas, rallied from a three-hole deficit with three to play to beat fifth-seeded Taffy Brower of Boynton Beach, Fla., in 20 holes.
Creekmore birdie two of the last three holes of regulation and won on the second playoff hole when Brower hit her approach into a hazard.
'I'm sure there must have been some comebacks before, but I can't ever remember having to birdie two of the last three holes to do it,' Creekmoore said.
The semifinals and finals are Thursday.