Depor remained rooted to the bottom of the table after the defeat at the Cornella El Prat stadium in Barcelona.
Victory for Espanyol lifted them out of the relegation places to 16th on 15 points from 17 matches.
They have now drawn three, including a 2-2 stalemate at champions Real Madrid last weekend, and won one in the four games since Javier Aguirre replaced the sacked Mauricio Pochettino as coach.
Simao opened the scoring in the 31st minute when goalkeeper German Lux punched clear only for the Portuguese to send a looping header back over his head into the net and Cristian Stuani snuffed out Depor's hopes in the 88th minute.
Oltra is in his second season in charge after guiding Depor back into top flight when they won the second division last term.
En route to the win, Espanyol had the ball for 42.5% of the match.
Periquitos had nine shots, including five on target.
The most effective of Espanyol's three substitutions was Raúl Baena, who, after replacing Víctor Sánchez in the 45th minute, assisted on Stuani's goal.
The three attempts by Sergio García were the most of any Espanyol player.
Deportivo de La Coruña maintained control of the ball for 57.5% of the match of the match, a testament to their movement and linking play in the open field.
Deportivo de La Coruña won 66 duels and 26 headers, which led to nine shots, including four on target.
Nélson Oliveira made a big difference on the match for Deportivo de La Coruña after coming on for Riki in the 61st minute due to injury, as he took two shots.
Riki had five shots for Deportivo de La Coruña, more than any of his team-mates.