Paco Alcacer looked to be in an offside position when he slid into convert a cross from Sofiane Feghouli to put Valencia ahead, while Aritz Aduriz levelled after Athletic had been awarded a soft penalty, Ander Herrera colliding with Feghouli in the area.
A draw was not the result either team wanted, and it means Valencia slip five points behind seventh-placed Sevilla, while Athletic were unable to take full advantage of Villarreal's defeat at Granada, and could only extend their lead on Marcelino's side in the race for fourth place to seven points.
The tone of this gripping match was set with less than a minute on the clock, when Aduriz missed the target from close range as he connected with a cross from Herrera, who then smashed a shot against the post from the edge of the area.
Valencia were also getting forward often, with Athletic defender Aymeric Laporte doing well to clear a deadly cross from the lively Juan Bernat before Jonas could strike at goal.
The hosts took the lead on 23 minutes, Joao Perreira playing in Feghouli down the right hand side, the Algerian's low cross turned in by Alcacer.
The Athletic players were furious the goal was allowed to stand, and replays showed that both Feghouli and Alcacer should have been ruled offside.
Athletic goalkeeper Gorka Iraizoz then kept out a dangerous cross-shot from Dani Parejo, and a minute later Fede Cartabia narrowly missed the target from 20 yards out.
Valencia had finished the first half the much stronger side but Athletic were allowed a way back into the game when Feghouli and Herrera came together to contest a cross at the far post, the referee ruling in favour of the visitors.
Aduriz calmly slotted into the bottom corner to score his fourth goal in two games.
Seydou Keita almost scored a sensational goal shortly after the hour mark for Valencia, controlling a pass from Jeremy Mathieu and turning a defender but shooting the wrong side of the post.
At the other end, Iker Muniain should have done better from a one-on-one effort with Diego Alves, the Valencia goalkeeper winning the duel.
Neither side looked happy to settle for a point, which made for a frantic finish, but the game finished with a goal apiece, the same result from when the two teams met in Bilbao earlier in the season.