Garcia, ranked 47th in the world, reeled off five consecutive games in the decider to beat the former world number one Angelique Kerber 3-6, 6-2, 6-4.
"There were lots of ups and downs in the match," said Garcia. "But I was in a positive mindset."
After moving into a 4-1 lead, Kerber appeared to tire and Garcia lured her into a series of errors.
"I was frustrated with my inconsistency," the 27-year-old added. "I would play a good point and then a terrible one. You can't do that especially against someone like Angelique."
Fortunately for Garcia, Kerber, who has fallen to 26 in the world rankings, was even more erratic and the famed doggedness that brought her top spot in the pecking order as well as three Grand Slam tournament titles deserted her.
"I'm pleased I kept fighting to get the win," Garcia added.
Mladenovic joined her in the second round after the world number 53 also overcame a higher ranked opponent.
Petra Martic, seeded 13th in the tournament on the back of her status in the top 30, had won the last five of her encounters with Mladenovic.
But after a tight first set, Mladenovic swept through the tiebreak seven points to two.
She took the second set 6-4 to move into a clash with the American Jessica Pegula who beat her last month in the third round at the Australian Open.
