Ferrer next plays qualifier Ivan Dodig, who defeated fellow Croatian Marin Cilic 6-2, 7-6 (6). Jurgen Melzer, who has not dropped a set in the tournament, and Alexandr Dolgopolov won and will meet in the semifinals.
The fifth-ranked Ferrer had little trouble on the hard indoor surface. He improved to 12-0 against an opponent who will become his teammate next month when Spain defends its Davis Cup title against the Czech Republic.
Ferrer has won the Valencia title twice and has never lost to Almagro. They played four times this season.
"It was my best game of the week," Ferrer said. "Today I knew had to play at my best level or I wouldn't win."
Almagro had a triple-break chance in the sixth game of the second set, but Ferrer held before breaking in the 11th game. Ferrer saved his fourth break point in the final game and won when Almagro hit long.
Melzer beat David Goffin of Belgium 7-6 (7), 6-4. The Austrian overcame a poor first serve, including seven double-faults.
Dolgopolov defeated defending champion Marcel Granollers 6-0, 6-2. The Ukrainian was perfect on his first serve in the first set.
"It was for sure easier than expected. He was frustrated and he wasn't playing his best tennis," said the 21st-ranked Dolgopolov, who broke the Spaniard five times.
"I had no chance of coming back," Granollers said.
Granollers reached the last two finals in Valencia and is expected to lead Spain's doubles team in Prague.