Third seed Garcia had a busy day, finishing off her second- round match against Slovakia's Jana Cepelova before returning later to beat Italy's Roberta Vinci.
Vinci had set points in the second set but Garcia avoided the potential for another match interrupted by bad light, as happened the previous night against Cepelova, as she scraped through a tense second-set tiebreak for a 6-2 7-6(8) win.
In the other half, Julia Goerges beat fellow German Sabine Lisicki 6-2 6-4 while American Catherine Bellis beat Kristyna Pliskova of the Czech Republic 6-3 6-2.
(Reporting by Martyn Herman, editing by Ed Osmond)
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