The 13th-ranked Ferrer will face fifth-seeded Jeremy Chardy, who beat Sebastien de Chaunac 7-6 (4), 6-3 in an all-French quarterfinal.
Ferrer broke Baghdatis in the 11th game of the first set when the Cypriot sent a backhand long. The Spaniard broke twice more in the second set and saved his only break-point chance.
Baghdatis had six double-faults.
Top-seeded Jo-Wilfried Tsonga of France plays Kristof Vliegen of Belgium and Guillermo Garcia-Lopez of Spain meets Frederico Gil of Portugal in the other quarterfinals later Friday.
Player Ratings: Barcelona 2-0 Real Mallorca
Ferrer, Chardy reach SA Tennis Open semifinals
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