The 33-year-old Blake, who was runner-up in the 2007 Cincinnati Masters, emerged from the first round with a 6-1, 7-5 upset of 16th-seeded Pole Jerzy Janowicz.
His next opponent will be Russian qualifier Dmitry Tursunov, who posted a 4-6, 7-6 (8-6), 6-4 triumph over Slovakia's Martin Klizan.
No. 13 Spaniard Almagro, meanwhile, was upended by Bulgarian Grigor Dimitrov 7-6 (7-3), 6-4 at the Lindner Family Tennis Center.
Also advancing in a surprise result Monday was 34-year-old Czech veteran Radek Stepanek, who dispatched No. 14 Italian Fabio Fognini, 6-2, 6-4. Fognini was seeking his third title of the season.
American wild card Brian Baker, Serbian Janko Tipsarevic, French qualifier Jeremy Chardy, Spaniard Marcel Granollers, Argentine Juan Monaco and Belgian David Goffin also completed Day 1 victories Monday.
Swim Week Miami Beach 2014 [PHOTOS]