The top-seeded American broke Rybarikova's serve at 5-4 to win the first set and quickly took control of the second to clinch the victory in 1 hour, 25 minutes at the hard court tournament in southern Brazil.
Williams faced nine break points to the 52nd-ranked Rybarikova but was broken only twice.
The 20th-ranked Williams is playing in her first tournament since losing to Maria Sharapova in the third round of the Australian Open in January.
Williams will next face Olga Puchkova of Russia, who cruised past Jana Cepelova of Slovakia 6-1, 6-1 despite eight double faults. The 109th-ranked Puchkova, who upset third-seeded Kirsten Flipkens of Belgium in the first round, will be trying to reach her first final since 2006.
The 58th-ranked Mladenovic, who has yet to lose a set, broke Czink's serve four times and saved eight break points to win the match.
Czink had eliminated second-seeded Yaroslava Shvedova of Kazakhstan in the first round and crowd-favorite Bia Haddad Maia in the second.
Niculescu reached the semis by beating Timea Babos of Hungary 6-3, 6-2. Niculescu lost the Luxembourg final to Williams last year, marking the American's most recent title.