The hosts started well and took the lead inside 17 minutes, as Carlos Vicente scored his second goal this season with a first-time finish that went under Orjan Nyland’s body after connecting with Nahuel Tenaglia’s pass.
Their advantage was almost doubled just three minutes later, as Toni Martinez lashed his strike just wide after chasing a ball over the top.
Alaves did have the ball in the net a second time through Stoichkov midway through the half, but his goal was ruled out for offside after tapping Martinez’s cross at the back post.
Saul Niguez came closest to drawing Sevilla level in the first half, but his header flashed wide from Adria Pedrosa’s cross.
It was a poor 45 minutes from the visitors, who suffered a further blow when Isaac Romero was forced off injured in the opening quarter-hour and was replaced by Kelechi Iheanacho.
Chasing an equaliser after the break, Saul had another chance to bring Sevilla level just before the hour-mark, but he could only poke his effort straight at Antonio Sivera after Dodi Lukebakio found him in the box.
His wastefulness would be punished immediately, as Carlos Martin netted his maiden LaLiga goal on his first start for Alaves, reacting well as Stoichkov’s header came back off the crossbar.
The latter forced Nyland into a smart stop shortly after, as momentum shifted back to Luis Garcia’s side.
Stoichkov is still waiting for his first Alaves goal after being substituted off, but the namesake of the great Hristo Stoichkov certainly impressed.
Just as the hosts were getting comfortable, Lukebakio struck back for Sevilla with a lovely curling effort into the bottom corner, meaning Alaves would be denied a home clean sheet for the first time this campaign.
Nonetheless, they managed to hold on for victory, stretching their unbeaten home record to seven games in the process.
It is clear that Sevilla are struggling under Garcia Pimienta, as the new manager is yet to get a tune out of his players.
Flashscore Man of the Match: Stoichkov (Alaves)
