Bogdan cruised to a 5-0 lead in the third set. Fernandez saved seven match points in a marathon seventh game, eventually pushing the set to an eighth, but Bogdan then finished the job, having capitalized on Fernandez's 11 double faults.
Czech third seed Katerina Siniakova and American sixth seed Peyton Stearns both needed three sets to advance. Siniakova rallied for a 6-7, 6-3, 7-6 victory over Japan's Sayaka Ishii, saving three match points in the ninth game of the third set as she dug out of a 5-1 hole.
Stearns beat Japan's Moyuka Uchijima 6-0, 1-6, 6-1 despite committing eight double faults and saving none of the four break points she faced.
In other action, Belgium's Greet Minnen and Spaniards Jessica Bouzas Maneiro and Sara Sorribes Tormo advance along with top seed Beatriz Haddad Maia.
Abierto GNP Seguros
Russia's Erika Andreeva won the final four games to upset top-seeded Danielle Collins of the United States 1-6, 6-3, 6-3 in the second round in Monterrey, Mexico.
Andreeva didn't face a break point in the third set while winning 83 per cent of her first-serve points.
The rest of the day's action consisted of first-round matches. Sixth-seeded Linda Noskova of the Czech Republic fell just short of recording a double bagel, routing Kazakhstani qualifier Anna Danilina 6-0, 6-1.
Noskova led 6-0, 5-0 before Danilina, ranked 958th in the world, finally held serve. The match lasted just 49 minutes, with Noskova never facing a break point.
China's Yue Yuan, the seventh seed, rallied past Serbia's Aleksandra Krunic 4-6, 6-2, 6-3, and ninth-seeded Magdalena Frech of Poland topped Argentina's Nadia Podoroska 6-4, 4-6, 6-4.
Other first-round winners were China's Xiyu Wang, Mexico's Renata Zarazua and Croatia's Petra Martic.