Goals from Javi Guerra and Alberto Bueno in the first 15 minutes put Miroslav Dukic's side in the ascendancy, but Oscar de Marcos' 21st-minute strike gave Athletic hope and then Markel Susaeta salvaged a draw for the visitors early in the second half.
The stalemate left Valladolid 10th in the standings - still three points and three positions better off than their opponents.
The hosts needed only eight minutes to take the lead, Guerra heading Antonio Rukavina's right-wing cross into the top-left corner.
Athletic, who headed into this game buoyed by last weekend's 3-0 mauling of second-placed Atletico Madrid at San Mames, almost got back on level terms seven minutes later when Aritz Aduriz's shot beat Dani Hernandez but he was denied by the post.
Moments later, Valladolid went up the other end and made it 2-0. Daniel Larsson provided the assist for Bueno to slot home from close range.
Athletic refused to lie down, though, and halved the deficit midway through the first half through De Marcos, who lashed an unstoppable volley past Hernandez from Susaeta's right-wing cross.
Hernandez had to be alert to preserve his team's lead just before the half-hour mark, parrying De Marcos' 30-yard left-footed volley.
Valladolid were forced into a change 10 minutes before the break when a bad challenge by Aduriz ended centre-back Marc Valiente's participation in the match, the Athletic man picking up a deserved yellow card.
Aduriz was at the centre of the action again four minutes after the restart, this time playing a key role in getting the Basque side back on level terms. His header fell perfectly for Susaeta, who directed a right-footed shot into the top-left corner.
Marcelo Bielsa's side could even have won it in the closing stages, but Susaeta fired wide while Ander Herrera and Ibai Gomez saw decent attempts saved by Hernandez as the game finished all square.