Kalu Uche could have given the home side the lead as he latched on to a free kick from El Zhar, but he failed to hit the target with his header from close range.
Espanyol took the lead right on the stroke of half time when Felipe Caicedo burst into the penalty are and blasted his strike into the top corner.
In the second half, the home side went right on the attack and Jose Luis Morales drilled an effort at goal from just outside the box, which went just wide of the target.
Espanyol tried to kill the game off and went close through attempts from Víctor Alvarez and Christian Stuani, but neither could hit the back of the net with their strikes.
Levante pushed late on for an equaliser and got their just rewards when Casadesus turned Uche's headed pass into the bottom corner from close range to earn his side an important point.