The fifth-seeded pair won through in a thrilling decider to take the match 7-5, 3-6, 10-3.
"We lost in a super tiebreaker and still I think we had lots of opportunities," said Mladenovic afterwards. "We had a big lead in the first set and I think we should have closed it out and won probably, but it's tennis, and the girls are playing well as well and in the third set anything can happen."
Mladenovic was not too disappointed, however, adding that she and Garcia were both working on their singles game while competing in doubles.
"It's not easy, it's just our second tournament of the year," she said. "I still think we had a good run in Melbourne - lost in the semis - here we had a tough tournament. It's our goal this year, we are going to be more focused on our singles and we are trying new things, like we are switching sides every set and like really working on our singles game."
The 23-year-old remains hopeful that she and her partner will impress over the course of the year.
"It's just the beginning of the season," she pointed out. "We are looking forward, the season is very long and Indian Wells, Miami coming up soon so everything is positive."