In an opening half of very few chances, the away side managed to break the deadlock with 37 minutes on the clock. Stuani and Verdu combined to free the latter, who found the back of the net from inside the area.
Any hope that the hosts held of getting back into the clash began to diminish when they lost their first player to a red card nine minutes after the restart. Spanish midfielder Borja was the guilty party, having been punished for handling the ball.
The away side made the most of their numerical advantage just one minute later when Argentine defender Diego Colotto sent a cushioned header into the path of Stuani, who converted from close range.
The result has lifted Espanyol up to 10th in the La Liga standings, while Getafe stay ninth.