Athletic's capacity to break down Elche, who had not conceded any goals in their previous five home games, was made harder by the strong wind blowing over the Martinez Valera stadium, but credit must go to Fran Escriba's men for starving the Basques of proper goalscoring chances.
However, it made for a turgid night of football.
The hosts had the better chances to score, including the first attempt of the night - Garry Rodrigues shooting well wide of goal with three minutes played.
Elche had the better of the early stages of the game, meaning Athletic were forced to resort to efforts from long range. Ander Herrera managed to hit a free-kick on target, but was not able to beat stopper Manu Herrera.
Elche forward Richmond Boakye got a lot closer to goal midway through the first half, arriving in the six-yard box to get on the end of a low cross from Rodrigues - but the forward lifted the ball over the bar.
Iker Muniain was put through at the other end two minutes before half-time, but was also unable to keep his shot down as he attempted to beat Herrera at his near post.
It was a different Herrera who had Elche's next chance - substitute Christian Herrera taking advantage of a slip from Mikel San Jose, but his shot was blocked by Aymeric Laporte.
Defender Domingo Cisma would waste the hosts' final opportunity to snatch a winner, aiming a free header into the hands of Athletic stopper Gorka Iraizoz, while Markel Susaeta's late free-kick came to nothing for the visitors, who have now not won away from home in their last three games.