Zuluaga won five of six games to close out the second set before a mix of powerful serving and crosscourt shots gave her a 4-0 lead in the third.
Joining the 25-year-old Colombian in the quarterfinals was Amy Frazier of the US.
Frazier, a two-time semifinalist in Hobart, was a 6-1, 6-4 winner over Spain's Anabel Medina Garrigues in a match plagued by disputed line calls.
Frazier next plays Maria Elena Camerin after the Italian beat fifth-seeded Maria Vento-Kabchi of Venezuela 7-6 (7), 2-6, 6-1.
Japan's Akiko Morigami also advanced to the quarterfinals with a 7-5, 6-2 win over Slovakian Martina Sucha.
Canberra Classic
Top-seeded Paola Suarez of Argentina had a mid-match lapse but recovered for a 6-3, 2-6, 6-1 win over Italian Antonella Serra Zanetti at the Canberra Classic tennis tournament.
With the first-round win, Suarez advanced directly to the quarterfinals after her second-round opponent, Sandra Kleinova of the Czech Republic, withdrew from the tournament with illness.
Kleinova, who beat qualifier Tatiana Panova 6-4, 6-3 in their first-round match, complained of illness on Tuesday morning and after a medical examination she was forced to withdraw with a bacterial infection.
Suarez is due to face the winner of a match between Arantxa Parra of Spain and seventh-seeded Marlene Weingartner of Germany in the quarters. That match is also dependent on a medical examination after Weingartner withdrew from doubles with an abdominal strain.
Conchita Martinez Granados of Spain defeated Jelena Kostanic of Croatia 6-4, 4-6, 7-6 (5).
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