However, five minutes later Mallorca restored parity through Alejandro Alfaro, who turned in a corner from just yards out.
Roberto Trashorras could have replied for Rayo immediately when he shot from outside the box, but he failed to keep his effort on target.
Piti had two chances in quick succession thereafter before Andrija Delibasic saw his attempt saved on the half-hour mark.
The opening minutes of the second half saw little action, although Rayo's Leo did have his effort from close range saved in the 55th minute.
Minutes later Mallorca's Alfaro shot wide from distance before Hemed failed to keep his header from Giovani dos Santos's cross on target.
Mallorca continued to dominate proceedings at home, as Geromel headed narrowly wide midway through the half.
However, it was Rayo who came closest to finding the winner in the final minutes of the contest, as Lass's effort from a difficult angle on the left came off the post after Jordi Figueras had sent him through with a good ball.
The result leaves Mallorca third from bottom in the table, while Rayo are now eighth.