The Spaniard downed Volandri in just over an hour as he storms closer to adding the Mexico trophy to the titles he picked up at Argentina and Brazil in the last two weeks.
Almagro converted five of his seven break points on his way to winning his 11th straight match. He faces Santiago Giraldo of Colombia in the quarterfinals.
"It will be tough match," Almagro said. "It's the quarterfinals and nobody gives you anything."
Top-seeded David Ferrer of Spain cruised past Santiago Gonzalez of Mexico 6-2, 6-2.
Other seeded men in the tournament had mixed results.
No. 4 Stanislas Wawrinka of Switzerland needed three set to defeat Fabio Fognini of Italy 5-7, 6-3, 7-5. Sixth-seeded Alexandr Dolgopolov of Ukraine has an easier time, winning over Carlos Berlocq of Argentina 6-1, 6-4.
Seventh-seeded Juan Monaco of Argentina advanced, defeating Pablo Cuevas of Uruguay 6-3, 6-4.
However, No. 5 Albert Montanes of Spain went out against Santiago Giraldo of Colombia 6-3, 6-4.
In a late match, Thomaz Belluci of Brazil rallied to beat Spaniard Ivan Navarro 1-6, 6-4, 6-3.
On the women's side in the combined ATP-WTA event, top-seeded Julia Goerges of Germany was eliminated by Anabel Medina Garrigues of Spain 6-4, 7-6 (8).
Three other seeded women fared better.
Third-seeded Greta Arn of Hungary defeated Renata Voracova of the Czech Republic 6-3, 2-6, 6-4.
Fourth-seeded Gisela Dulko of Argentina defeated Silvia Soler Espinosa of Spain, 6-1, 6-1, and No. 6 Arantxa Parra Santonja of Spain won her match when Lesia Tsurenko of Ukraine retired in the second set while trailing 6-3, 1-0.
Seventh-seeded Carla Suarez Navarro of Spain downed Madalina Gojnea of Romania 6-4, 6-3.
Almagro reaches quarterfinals in Mexico
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