A goal by Joan Verdu gave the visitors the lead towards the end of a first half which saw few chances and little incident or excitement.
The hosts failed to produce the commanding performance coach Luis Garcia had demanded before the game, and their level dropped even further when Borja Fernandez was sent off early in the second half.
Getafe centre-back Federico Fernandez then also received his marching orders midway through the second period before Espanyol midfielder Christian Stuani made sure of the points immediately after with his side's second goal.
It took over 20 minutes for the first real chance of the game to arrive, with Getafe's Paco Alcacer sending in a cross to the six-yard box which Angel Lafita narrowly failed to get on the end of.
Alcacer had a better opportunity 10 minutes later, finding himself one-on-one with Cristian Alvarez, but he could only shoot straight at the Espanyol goalkeeper.
Espanyol broke the deadlock after 37 minutes thanks to a wonderful team move.
Verdu began the attack and then gave the ball to Stuani. The midfielder chipped a cross to Sergio Garcia, and the forward aimed a cushioned header into the path of Verdu, who shot past Jordi Codina with ease.
Getafe had the ball in the net not long after when Alberto Lopo headed in a free-kick, but the effort was ruled out for offside.
Borja made things even more difficult for his already struggling side when he received his second yellow card of the game in the 52nd minute for inexplicably picking the ball up after falling over while the game was still in play.
Garcia missed an opportunity to double the lead when he sent a free header wide of goal but Getafe made the visitors' day even easier when Fernandez pushed over an Espanyol player to earn his second yellow card of the game with 18 minutes remaining.
Wakaso Mubarak took the resulting free-kick, sending in a cross towards Diego Colotto, who cut the ball back for Stuani to finish off from a few yards out.
Getafe's efforts to try and get back into the game vanished there and then and in the end they were grateful to Codina for keeping the scoreline dignified.
Luis Garcia's side missed the opportunity to move above Rayo Vallecano and into eighth position in the Primera Division table, and they are now just one point above Espanyol.
The Catalans have now racked up 43 points that all but guarantees them survival, an objective that seemed far away when Javier Aguirre took charge of the club at the end of November.