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Bilbao are the fourth oldest Spanish club and among three never to be relegated, alongside Real Madrid and Barcelona.
Atletico lead the table on 73 points but third-placed Barca, on 71 after beating Villarreal 2-1 earlier on Sunday, can take over first place if they beat Granada on Thursday in their game in hand.
Messi scored twice as Barcelona thrashed Athletic Bilbao 4-0 in the Copa del Rey final on Saturday to win the trophy for a record-extending 31st time with all the goals coming in the last half an hour.
Messi was sent off for the first time in his Barcelona career in the closing stages of extra time as they lost 3-2 to Athletic Bilbao.
Raul Garcia scored twice in a 2-1 win over Real Madrid on Thursday to knock the holders out of the Spanish Super Cup and set up a final against Barcelona.
Barca were beaten 1-0 by Bilbao at San Mames, where Inaki Williams headed in a dramatic 93rd-minute winner, after La Real had seen off Madrid 4-3 in a seven-goal thriller at the Santiago Bernabeu.
The hard-fought win took Zinedine Zidane's side on to 77 points after 34 games, seven clear of second-placed Barca.
The victory left Real, who had drawn with Leganes in their last outing, in third place on 64 points.
Barca's all-time top scorer and captain Messi injured his calf in training before his side's brief pre-season tour of the United States and has not yet returned to full training.
The 38-year-old came off the bench late in the game and soon made Barca pay for squandering several chances by acrobatically lashing an unstoppable shot into the net in the 89th minute.
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