The Valencia-based outfit went into the match level on points with 18th-placed Almeria, aiming to put daylight between themselves and the relegation zone.
However, the hosts rarely looked capable of stealing all three points, as Espanyol forced them to come from behind twice in front of their own fans.
Lucas Vazquez, who has impressed on loan from Real Madrid this term, opened the scoring in the 18th minute for the away side, finding the bottom-right corner after creating space for himself inside the area.
Levante hit back through Simao Mate three minutes later, the Mozambique internaional nodding in from a corner, only for in-form Felipe Caicedo to restore Espanyol's lead just before the break, holding off Juanfran to find the net against his former team.
Espanyol could not hold on, though, as Victor latched on to Kalu Uche's flick-on and slammed home from 14 yards three minutes from time to earn Levante a point, and dent the visitors already-slim chances of UEFA Europa League qualification.
