Three goals in six first-half minutes had promised a free-scoring match but after the early excitement there was precious little for the fans at Campo de Futbol de Vallecas.
Andrija Delibasic put the hosts ahead in the seventh minute but their lead was short-lived with Raoul Loe equalising a minute later before Alejandro Arribas gave the visitors a surprise lead.
Piti equalised 12 minutes into the second half but a point does little for Rayo as it leaves them four points behind sixth-placed Malaga, who occupy the final European spot.
Rayo made an ideal start as they took a seventh-minute lead with the first attack of the game.
Alhassane Bangoura's cross from the right found Delibasic in the six-yard box and he headed the ball down into the left-hand corner of the goal.
However, the hosts' joy was short-lived with the visitors equalising just 71 seconds later.
Alvaro Cejudo sent in an outswinging corner from the right which Loe attacked, heading high into the net.
The breathless start continued unabated and after having found themselves a goal down, Osasuna found themselves 2-1 up in the 13th minute.
Miguel De las Cuevas' shot was saved by Martinez Ruben and from the subsequent corner, David Timor found Arribas at the far post with the midfielder heading into the bottom corner.
After such an intense opening, it was naturally going to settle down with no clear opportunities created by either side in the remainder of the first half.
Piti fired wide for Rayo shortly after the resumption before Jose Carlos' shot from distance was comfortably held by Osasuna goalkeeper Andres Fernandez.
Rayo drew level in the 57th minute when Piti was found by Alejandro Dominguez and the striker slotted into the bottom left-hand corner.
Francisco Silva's shot was comfortably gathered by Ruben but there was precious little in attacking play as the clock ticked down.