It might have been even worse for the Galician side after they found themselves on the back foot for much of the first half and then reduced to 10 men in the closing stages when veteran defender Carlos Marchena was sent off.
However, there was not enough time for Rayo to make the most of their extra man as the points were shared at the Riazor.
The result leaves Depor eight points adrift of Real Zaragoza and safety, while Rayo move back into eighth place.
Both teams came into the match in poor form, Depor without a point since January 13 and Rayo having lost three of their last four, but the visitors looked the more likely to get back on track on Saturday following a one-sided first half.
Rayo striker Alhassane Bangoura spurned a one-on-one chance in the 12th minute before Depor goalkeeper Daniel Aranzubia produced two fine saves to keep out efforts from Jose Manuel Casado and Roberto Trashorras.
The visitors continued to push forward and Bangoura saw a shot come back off the post in the 23rd minute before being denied soon after by another crucial block from Aranzubia.
Depor tried to respond with an effort from Alexandre which was saved by Ruben Martinez before Bangoura spurned another opportunity just before half-time for Rayo.
The home side came into the game more in the second half and Ruben produced brilliant saves to keep out shots from Luis Pizzi and Diogo Salomao while Marchena and Salomao also saw efforts go over the bar.
However, Depor were left hanging on in the end when Marchena was shown a second yellow card in the 85th minute following a foul on Trashorras.
Rayo almost took advantage but Aranzubia tipped over Piti's shot as the game finished goalless.