Both goals came in the first 13 minutes with Piti putting Rayo ahead in the seventh minute only for Alejandro Alfaro to level six minutes later.
While Mallorca presented more of an attacking force, they were relieved to see the post twice come to their aid when the woodwork denied Alhassane Bangoura in quick succession.
Mallorca started the game second from bottom but just one point from safety after victory over Celta Vigo last time out had given them hope they could escape relegation.
Giovani Dos Santos had bundled the ball home in injury time to lift Mallorca from the foot of the table and leave Celta four points from safety.
A positive start, therefore, would have been what Mallorca were looking for but they found themselves a goal down in only the seventh minute.
Jose Manuel Casado's cross from the left wing found Piti who volleyed a left-footed shot into the bottom right of the goal from 18 yards.
However, it took just six minutes for the hosts to draw level.
Dos Santos' corner was headed goalwards by Alfaro and although Rayo goalkeeper Martinez Ruben managed to parry the ball, Alfaro pounced to shoot home from close range.
After such a breathless start, the game settled down with neither side carving out a clear-cut chance until the 28th minute when another Dos Santos corner found Tomer Hemed with the striker's header tipped round the post by Ruben.
Andrija Delibasic's shot was blocked by Mallorca goalkeeper Juan Calatayud before Triguero Tito fired over and Hemed's header was comfortably gathered as the hosts pressed but the break came without further goals.
Rayo had the best chance in the early stages of the second half when Leo Baptistao's shot from the centre of the area was tipped round the post by Calatayud.
Alfaro fired wide and Mallorca almost took the lead midway through the half and again Dos Santos was involved, this time his free-kick was tipped round the post by Ruben.
Pedro Geromel fired wide from a Dos Santos corner but the hosts breathed a sigh of relief when Bangoura's shot hit the post.
The same player then drilled in a free-kick from 25 yards which also came back off the woodwork.
Michael Pereira had a curling effort gathered by Ruben and Dos Santos fired wide with Roberto Trashorras putting a shot past the post for Rayo in injury time.
However, neither side could find the breakthrough and both had to settle for a point.