Atletico, who have won only one of their last six games in all competitions, are third in the standings on 24 points, eight behind Real Madrid who play Rayo Vallecano on Monday and 10 adrift of leaders Barcelona.
Espanyol remained 16th, one point clear of the relegation zone.
Despite playing most of the match with 10 men after defender Leandro Cabrera was shown a straight red card for a last-man foul on Alvaro Morata, Espanyol defended well.
They also made the most of their only shot on target in the second half when Sergi Darder was set up by a Joselu header to volley home in the 66th minute.
Substitute Joao Felix rescued a point for Atletico in the 78th minute, slotting a precise shot into the bottom corner following a counter-attack.