Almagro grabbed the decisive break in the eighth game of the deciding set and the Spaniard will fancy his chances of securing a 13th clay-court title of his career in his first appearance at the Houston tournament.
Fifth seed John Isner defeated 20-year-old fellow American wild card Jack Sock 7-5 6-7 7-6 in a match which featured just one break of serve.
Isner is aiming to reach his third semi-final of 2013, following Delray Beach and San Jose, but first he must deal with Lithuanian Ricardas Berankis.
The 73rd-ranked Berankis produced an upset beating 2004 Houston winner and number two seed Tommy Haas 6-3 6-3.
The 35-year-old German Haas stumbled after his fine effort at the Sony Open last month where he defeated world number one Novak Djkovic.
Third seed and defending champion Juan Monaco made his way safely through his opener, beating American Tim Smyczek 7-6 6-1.
American Rhyne Williams reached his first ATP World Tour quarter-final by defeating 2007 Houston champion Ivo Karlovic of Croatia 6-4 6-7 7-6.
US Clay Court Championship results
3-Juan Monaco (Argentina) beat Tim Smyczek (U.S.) 7-6(5) 6-1
Ricardas Berankis (Lithuania) beat 2-Tommy Haas (Germany) 6-3 6-3
Robby Ginepri (U.S.) beat Martin Alund (Argentina) 6-2 4-6 6-4
1-Nicolas Almagro (Spain) beat Gael Monfils (France) 2-6 6-0 6-3
5-John Isner (U.S.) beat Jack Sock (U.S.) 7-5 6-7(3) 7-6(3)
7-Paolo Lorenzi (Italy) beat Flavio Cipolla (Italy) 7-6(4) 6-1
Ruben Ramirez Hidalgo (Spain) beat 6-Fernando Verdasco (Spain) 6-3 6-2
Rhyne Williams (U.S.) beat Ivo Karlovic (Croatia) 6-4 6-7(5) 7-6(3)
Casablanca Open results
7-Robin Haase (Netherlands) beat Kenny De Schepper (France) 6-2 6-7(2) 6-3
3-Martin Klizan (Slovakia) beat Filippo Volandri (Italy) 6-4 7-6(5)
2-Kevin Anderson (South Africa) beat Pablo Carreno (Spain) 6-3 6-3
8-Grega Zemlja (Slovenia) beat Henri Laaksonen (Switzerland) 7-6(5) 6-1
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