The result means Ernesto Valverde's have now not lost for six games, although that statistic could have been different after Elche gave a good account of themselves at the Estadio Martínez Valero.
The home side, who had claimed just a solitary point from their last three league games, enjoyed the better of the chances but ultimately lacked a killer instinct to break down Athletic's resolute defence.
A point for Francisco Escriba's sees them remain in 14th place, while Athletic stay alone in fourth, nine points ahead of fifth-placed Sevilla and 13 off Barcelona in third.
In the night's other match, Espanyol beat Malaga 2-1 at La Rosaleda thanks to Pizzi's second-half strike.
Sergio Garcia had put the visitors ahead on 33 minutes only to see Pablo Perez level immediately for the hosts.
But Pizzi put Espanyol into the lead again when he swooped with 14 minutes remaining with what proved to be a decisive blow.
- Sports & Recreation
- Ernesto Valverde