Martic, who struggled through an error-riddled match against Kateryna Bondarenko in the second round, was again often her own worst enemy, allowing her 20-year-old Russian opponent to stay in the contest.
The world number one impressed in a highly-entertaining quarter-final that saw her fire 39 winners en route to a 7-6 (8/6), 3-6, 6-3 win against Martic.
Karolina Pliskova won 74% of her first service points, fired seven aces and broke the Croatian four times in a rain-interrupted match that was initially delayed by more than five hours due to heavy rain.
Mladenovic, the world number 49, kept things tight against Garcia, who is ranked 18 places higher, winning 71% of her first serve points and hitting 17 winners.