In a frantic start to the game, Jhon Cordoba opened the scoring for the visitors inside three minutes, but Paco Alcacer levelled only four minutes later.
A header from Jonas put Juan Antonio Pizzi's side in front on 32 minutes, but Cordoba won a penalty just before the break, allowing Sergio Garcia to equalise.
The two teams remain as they were before the game in the Primera Division table, with Espanyol one point above Valencia in eighth place.
The game had barely kicked off and Espanyol were ahead. Sergio Garcia laid the ball off to Cordoba on the edge of the area, and the Colombian controlled it before unleashing a terrific left-footed drive low into the bottom corner.
But Valencia responded quickly. Ever Banega chipped the ball into the box towards Jonas, who did not touch it, and instead Alcacer brought the ball down with his chest before steering it into the net.
Neither side took control of the game, but the hosts went ahead around the half hour mark, Jonas powering home a header from a corner.
Alcacer then misdirected a header wide, failing to double his side's lead, and lived to regret it as Espanyol were awarded a penalty right before half-time.
Jeremy Mathieu dispossessed Cordoba in the area but then lost the ball again and tripped the Colombian, who was headed away from goal. Garcia sent the penalty high into the top left hand corner.
Valencia could have scored just after the break, with Dani Parejo, Jonas and Piatti failing to get on the end of a cross from Joao Perreira.
At the other end, Cordoba nearly scored a goal reminiscent of Ronaldo's famous effort for Barcelona against Compostela, charging towards goal from the halfway line but dragging his shot just wide of the far post.
Michel then almost scored a late winner for the hosts, drilling the ball towards the top corner from the edge of the area, but Kiko Casilla flung himself across to punch the ball clear to preserve a point for his side.