Sergio García scored for the Periquitos in the 23rd minute, putting a left foot shot into the lower left of the goal after receiving a pass from Christian Stuani.
Espanyol have a record of four wins, nine losses and six draws this season, which puts them in 16th place, only one point above the relegation zone.
Celta de Vigo are in 15th place, just one point above the relegation zone with a record of five wins, 11 losses and three draws after 19 games.
Sergio García was on the pitch for 90 minutes, the striker took four shots.
En route to the win, Los Blanquiazules had the ball for 39.1% of the match.
Espanyol had 14 shots, including four on target.
Cristian Alfonso made his mark on the match for Periquitos after coming on for Joan Verdú in the 77th minute, as he took two shots.
Celta's players linked up for 372 passes and 26 crosses in defeat.
The six attempts by Iago Aspas were the most of any Celta player.