Javi Guerra nodded the home side in front in the eighth minute of an entertaining match between the two mid-table teams at Valladolid's rain-lashed Jose Zorrilla stadium.
Bilbao striker Aritz Aduriz shot against the frame of the goal in the 15th minute but moments later Valladolid were 2-0 ahead when Alberto Bueno turned in a Daniel Larsson centre.
Oscar de Marcos began Bilbao's fight-back in the 22nd when he volleyed Markel Susaeta's cross in off a post and Susaeta tapped in the equaliser at a corner five minutes after the break.
Bilbao have failed to reproduce the form that took them to the final of the Europa League and Copa del Rey last season.
Friday's draw leaves them in 13th place on 26 points from 22 matches with Valladolid 10th on 29 points.
"We got off to a poor start falling two goals behind," Susaeta told Marca TV.
"But the team is full of desire and we want to keep up the effort to climb up the table," he added.
Real Madrid, whose title defence has faltered leaving them 15 points adrift of leaders Barcelona, can move within a point of second-placed Atletico Madrid by beating Granada on Saturday.
Barca play at seventh-placed Valencia on Sunday before Atletico host Real Betis, who are fifth.
Real Valladolid had possession for 45.0% of the match.
Real Valladolid had 10 shots, including three on target.
The three attempts by Javi Guerra were the most of any Real Valladolid player.
Jesús Rueda was brought on to replace Marc Valiente in the 38th minute when the latter went down with an injury.
Athletic Bilbao controlled the ball for 55.0% of the match.
Los Rojiblancos had 18 shots, including nine on target.
Ander had five shots for Athletic Bilbao, more than any of his team-mates.
The combination of Iraola to Susaeta was the most common during the match, as the two players connected 17 times.
- Sports & Recreation
- Markel Susaeta
- Real Valladolid
- Athletic Bilbao