Sergio Garcia scored with almost the last kick of the game after two late goals looked to have earned the visitors the win.
The hosts took the lead in first-half stoppage time when Wakaso Mubarak headed in Garcia's cross.
Valencia nearly got themselves in front 10 minutes later, but Roberto Soldado saw his effort smash the post.
Espanyol netted what they thought was the winner with eight minutes left on the clock when Joan Verdu emphatically converted Wakaso's knockdown.
However, Jonas swept the ball into the bottom corner in the 88th minute to draw the visitors level once again.
Soldado then found the net on 91 minutes to make it 3-2 to Valencia before Espanyol substitute Raul Rodriguez was sent off for dissent.
With time running out, Garcia popped up inside the box to fire home and earn the home side an unlikely point.