After an even first set, the Polish player got the better of his opponent to come through 7-6 6-3 6-4.
Both players enjoyed a break of serve in the first set, but they could not be separated as it entered a tie-break, which the number 24 seed won 8-6.
The second set followed a similar pattern until the eighth game, when Janowicz broke the Spaniard to move 5-3 ahead. He held his serve in the next game to take the set 6-3.
Janowicz and Almagro continued to serve well, with Janovicz winning two love games in a row. However, in the ninth game the Pole made a crucial break before serving out the match 6-4.