The away side came close to opening the scoring after seven minutes, but Jhon Cordoba's effort was tipped onto the crossbar by the goalkeeper.
Espanyol continued to push forward and Sergio Garcia came close five minutes later, although his drive towards goal was saved again by the goalkeeper.
Verza stepped up a slotted the ball into the bottom corner, but the referee ordered a retake for an infringement inside the box. Verza then dramatically fired his second attempt over the bar to keep the score level at 0-0.
Following the missed spot kick, the hosts began to dominate the game and pushed Espanyol back into their own half.
Espanyol had a chance to take the lead early in the second half from a free kick on the edge of the area, although Torje sent the shot just wide of the post.
The visitors stayed on top for much of the second half and came close through Garcia on 62 minutes, but his strike went over the bar.
Almeria's best chance of the second period came on 69 minutes when Nelson Marcos fired across the box, causing confusion between the defence and goalkeeper before being cleared.
Thievy Bifouma had a good opportunity to claim all three points in injury time, but his strike from a cross went wide of the mark.