Larsson struggled for more than 2 hours but managed to outlast France's Irena Pavlovic 4-6, 6-4, 7-5 on the indoor hard courts of the Racquet Club of Memphis.
But Slovakia's Rybarikova, the defending Memphis champion, couldn't overcome American qualifier Jamie Hampton, falling 7-6 (9-7), 6-0.
Hampton didn't allow Rybarikova a break opportunity in the second set.
Also in Memphis Sunday, Italian Alberta Brianti got past Croatian Mirjana Lucic 7-6 (7-5), 5-7, 6-1, and Olga Govortsova upended Russian Vesna Dolonts 6-1, 7-5.
Celebrity Families of 2014 [PHOTOS]