The hosts had a golden opportunity to take the lead in the first half, but Rubén Vargas failed to convert a penalty as Alavés goalkeeper Antonio Sivera produced an important save.
Sevilla started the contest with attacking intent, while Alavés looked dangerous on the counterattack. The visitors created an early opportunity through Yusi, whose effort from Ángel Pérez's cross went narrowly wide.
The biggest moment of the first half arrived around the half-hour mark when Sevilla were awarded a penalty after Félix Correia was brought down by Ángel Pérez.
Vargas stepped forward to take the spot-kick but his powerful effort lacked sufficient placement, allowing Sivera to dive and keep the ball out.
Sevilla continued to search for an opener, with Juan Iglesias seeing his effort cleared off the line by Pablo Ibáñez. Félix Correia also came close after a promising attacking move, but his curling attempt drifted narrowly wide.
The home side increased their pressure after the restart, forcing Alavés to defend deep. Iglesias threatened again with a header that required another intervention from Sivera.
Alavés gradually found opportunities of their own, with Benavídez coming close from a goalmouth scramble in the 73rd minute.
Both managers introduced fresh players in search of a breakthrough, but neither side could find the decisive goal as the contest ended without a winner.
The result extended Alavés' winless run at the Ramón Sánchez-Pizjuán to eight matches, while Sevilla were left disappointed after failing to make their home advantage count.
Before kick-off, both teams paid tribute to Tenerife player Jesús de Miguel, who died earlier in the week. The match was also stopped in the ninth minute in his memory.
Result: Sevilla 0-0 Deportivo Alavés
Key moment: Rubén Vargas' missed penalty, saved by Antonio Sivera around the 32nd minute.
Venue: Ramón Sánchez-Pizjuán Stadium, Seville.
Competition: LaLiga, Matchday 12.