Athletic lost striker Aritz Aduriz to a red card after just 10 minutes and Rayo looked set to make their opponents pay a heavy price as they went ahead almost immediately through Franco Vazquez.
The visitors hit back, however, and goals from Markel Susaeta and Jon Aurtenetxe saw them leading just after half-time.
Rayo made it 2-2 through Piti before the hour but they could not go on to force a winner as the points were shared.
The Madrid-based side, who could have claimed seventh spot if they had beaten Athletic and Real Betis had lost to Levante, must now wait to see if they will be able to play Europa League football next season.
Their future is uncertain after the Spanish Football Federation denied them the UEFA licence they need to compete in Europe because of outstanding debts.
The club have declared their intention to take their case to the Court of Arbitration for Sport if they qualify for Europe and if they had finished seventh they would in theory have been entitled to an automatic place in the Europa League. Eighth place could yet see them qualify for Europe if Malaga's UEFA ban is upheld, and Rayo's is lifted.
Athletic, who were playing for little but pride having banished their relegation fears a few weeks ago, started promisingly and almost took a seventh-minute lead only for Ibai Gomez's shot to hit the post.
They suffered a major setback moments later, though, as Aduriz, having been booked in the fourth minute, was handed his marching orders for a foul on Alejandro Galvez.
Rayo did not take long to make the most of their numerical advantage as Franco Vazquez headed them into an 18th-minute lead.
Athletic refused to go down without a fight, though, and they hit back in superb fashion to take the lead.
The visitors almost drew level in the 24th minute when Oscar De Marcos saw an effort tipped over by Ruben Martinez, but they needed to wait only six minutes later when Susaeta got on the end of a Gomez cross to divert home.
Athletic then went ahead three minutes into the second half following another Gomez ball into the box, Aurtenetxe the man to finish it off this time.
The Basque side were not in front for long, though, as Rayo made it 2-2 in the 55th minute through Piti.
That left Rayo with over half an hour to try and find another goal to win the game, but they were unable to manage it as the 10 men of Bilbao held on for a battling draw.