American Querrey, ranked 36, fired 10 aces in beating the 19th-ranked Almagro to reach his fifth ATP semifinal, his first since July.
Playing with confidence behind a powerful and accurate serve, Querrey was able to take chances in return games, capturing breaks in the first and ninth games of the first set and the sixth and eighth games of the second.
His court movement was much swifter and more decisive than in previous matches this week and his long reach squeezed Almagro's passing options.
"I think that (first) game set the tone for the rest of the match, so fortunately I won it,'' he said. "I'm going out and trying to be aggressive. This is the best I've played in a long time.''
Querrey will face another Spanish player, second-seeded David Ferrer, in Friday's semifinals. Ferrer advanced on a walkover when defending champion Philipp Kohlschreiber withdrew because of a shoulder injury.
Kohlschreiber played with the help of painkilling injections in his second-round match on Wednesday but informed tournament organizers Thursday he could not continue.
"It was not easy to make the decision,'' he said. "Everyone likes to play in the quarterfinals and the tournament is just getting interesting so it makes me very sad.''
Top-seeded Juan Martin Del Potro of Argentina reached the semifinals with a 6-3, 6-2 win over Viktor Troicki of Serbia.
Del Potro gained a service break in the second game and held serve to take the first set in 42 minutes. He broke Troicki in the first and third games of the second set but lost his serve in the sixth game before clinching the set in 41 minutes.
Del Potro will play the winner of Thursday's late quarterfinal between third-seeded Robin Soderling of Sweden and American qualifier John Isner.
"Tomorrow I will have a tough match for sure but if I play my game I can win so I have to be focused on my play,'' he said.
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