France’s world number 29 Garcia won the first-set on a tie-break and subsequently did not drop another game as she wrapped up a 7-6 (7/2) 6-0 triumph in 88 minutes.
Garcia will play compatriot Kristina Mladenovic for a place in the last four.
Seventh seed Daniela Hantuchova will not feature in the quarter-finals, however, after she slumped to a straight-sets defeat to Urszula Radwanska.
Slovakian world number 46 Hantuchova was thoroughly outclassed as her Polish opponent, ranked 95 places lower, needed just 75 minutes to secure a 6-2 6-4 win.
Radwanska will meet Timea Bacsinszky in the quarter-finals after the Swiss fourth seed ended Ukrainian Lesia Tsurenko’s interest in the tournament.
Bacsinszky lost the first set 4-6 but regained her composure to win the next two by the same scoreline to wrap up a 4-6 6-4 6-4 victory in a match lasting more than two-and-a-half hours.
Fifth seed Anastasia Pavlyuchenkova set up a quarter-final showdown against second seed Sara Errani after overcoming Johanna Larsson 6-4 6-4.