Slovakia's Rybarikova was quickly ousted by Croatian Ajla Tomljanovic 6-1, 6-3 on the clay courts of the Fairmont Acapulco Princess.
The news was better for Jovanovski, however, who made the second round with a comeback 3-6, 7-6 (7-5), 6-4 win over American Tornado Alicia Black.
In another upset of a seeded player, No. 7 Stefanie Voegele of Switzerland was bounced by Japan's Kimiko Date-Krumm 3-6, 7-6 (7-5), 6-4 margin.
American Christina McHale and Marina Erakovic of New Zealand also each notched an opening-round victory.
Notable deaths of 2014 [PHOTOS]