Andreeva, ranked 194th in the world, saved five of the six break points she faced against world number 49 Fernandez of Canada. She will face Brazil's Beatriz Haddad Maia in the second round later on Thursday at the claycourt tournament.
"It was really tough match for me and I just tried to give my best and to play every point," said Andreeva, who also became only the second 15-year-old to defeat a Top 50 opponent at a WTA 1000 tournament.
"I'm extremely happy with my level today."
Andreeva said she had needed time to recover from her defeat in the Australian Open girls' final earlier this year, where she lost the match after winning the first set.
"My coach said to me after maybe five years you will not even remember that you played the Australian Open final or against who. It kind of helped me a little bit. Still, I remember it and it hurts, but now it's in the past," she said.
Andreeva's older sister Erika (18) also plays on the WTA Tour.
