Manuel Pellegrini's side had the better chances but two headers from Martin Demichelis failed to find the target in the first half, while home goalkeeper Cristian Alvarez was called upon in stoppage time to turn Roque Santa Cruz's header wide.
The draw does neither side much good as Espanyol remain in La Liga's relegation zone, while Malaga could lose further ground on leaders Barcelona and Atletico Madrid if results go against them.
Pellegrini opted to rest winger Joaquin, who had been Malaga's match winner in the previous two games, and his invention was missed in a first half devoid of chances from open play.
Those that did arrive came from set-pieces, as Juan Forlin nodded just wide for the hosts on six minutes before Demichelis really ought to have scored eight minutes later, but completely mistimed his header from inside the six yard box.
The Argentinian defender had another chance from a Duda free-kick just before half-time but, despite making a better contact this time, his effort still flew beyond the far post.
Pellegrini introduced Joaquin for Seba Fernandez on the hour, but it was Espanyol who were carrying the greater threat at the beginning of the second half.
And Mubarak Wakaso should have done better when presented with a clear shooting opportunity inside the area but he blazed over.
Malaga could have snatched the points in stoppage time as Jesus Gamez galloped down the right and picked out Santa Cruz, but Alvarez got down well to turn his low header round the post and ensure a point for his side.