Almagro hit 18 aces to Potito Starace's three but went serve for serve with the Italian before finishing off a 7-6 (1), 6-7 (5), 6-3 win. Almagro made the decisive break for 4-2 in the third set.
"It was a tough match,'' fourth-seeded Almagro said. "I played a good first set and a better tiebreak than him. In the second set I couldn't take advantage of the early break I had in the second set. I'm still not playing as good as last year but am getting better each match.''
In his fourth successive quarterfinals in Acapulco, Almagro will play Spanish countryman Daniel Gimeno-Traver.
Not so fortunate was compatriot and eighth-seeded Moya, the champion in 2002 and 2004 and a finalist two years ago. Meeting 110th-ranked Leonardo Mayer of Argentina for the first time, Moya lost 6-4, 7-5, squandering four break chances.
Moya made only half of his first serves and was broken once in each set to bow out in the second round for the second year in a row. Mayer, following only his sixth ever match on the main ATP Tour, will meet second-seeded Gael Monfils after the Frenchman outlasted Thomaz Bellucci of Brazil 7-6 (4), 6-7 (5), 6-1.
Two other Spanish seeds also departed; Gimeno-Traver ousted No. 6 Albert Montanes 7-6 (5), 7-6 (5), and Martin Vassallo Arguello of Argentina removed No. 7 Marcel Granollers 6-4, 6-3 to reach his first quarterfinals in two years.
However, third-seeded Tommy Robredo of Spain, the champion this month in Brazil and Argentina, routed Kevin Kim of the United States 6-2, 6-0 in 44 minutes.
In the women's draw, both of the Bogota finalists last weekend were ousted.
Eighth-seeded Maria Jose Martinez Sanchez of Spain, who won her first WTA title in Bogota, was tripped up by Petra Cetkovska of the Czech Republic 3-6, 6-4, 6-1 for a third time, while fifth-seeded Gisela Dulko, the Bogota runner-up, was upset by Maret Ani of Estonia 7-6 (6), 6-3.
Iveta Benesova, the champion five years ago, survived Klara Zakopalova 4-6, 6-4, 7-6 (3), in an all-Czech match, but two more seeds exited in the second round.
Third-seeded Carla Suarez Navarro, the Australian Open quarterfinalist, lost to Barbora Zahlavova Strycova of the Czech Republic 6-4, 7-5, and seventh-seeded Tathiana Garbin withdrew with a bad abdominal strain before her match against Mathilde Johansson of France. Johansson will play Benesova in the quarterfinals.
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