Juan Iglesias struck in the 81st minute, heading home a loose ball after Felix Correia's free kick was only half cleared, to settle a tight contest at the Ramon Sanchez-Pizjuan and move Sevilla up to third in LaLiga on 10 points from five games. Valencia, who had goalkeeper Stole Dimitrievski to thank for keeping the scoreline level for so long with saves from Kike Salas and Fofana, remain bottom of the table with a single point from their opening five matches.
Sevilla boss Luis Garcia Plaza, whose side have made one of the best starts in LaLiga this season, said his side's control of the second half was ultimately decisive.
"It was a difficult start and the team is responding wonderfully. I think it was a match of persistence, and in the second half we barely let them past midfield. In the one instance they did, you can lose, but the team deserved the goal much earlier," Garcia Plaza said.
"We played almost the entire match in their half. In the first half not so much, because they were also better, but as soon as we adjusted two things, especially around the hydration break, it was about attacking, winning the ball back and attacking again. We did half an hour at a very high level, but we lacked a bit of inspiration."
Valencia head coach Carlos Corberan, whose position has come under increasing scrutiny, admitted his side had been second-best after the break.
"That's exactly it, the truth is in the end it was a completely unwanted result on our part, and a match where we managed to level the first half, but where we were overwhelmed in the second half and we didn't find a way to change the emotions," Corberan said.
"It's true that just before their goal we had the chance to put the team ahead, we didn't take it, and they were able to score from a set piece that made the difference in a second half where Sevilla were better than us."
Asked how his side could turn their season around, Corberan pointed to Tuesday's trip to Alaves as the immediate priority, with his side seeking their first win of the campaign.
"In this moment of pain there is nothing else to do but learn, analyse and draw conclusions, because I am the one responsible for trying to make the team do things better to achieve better results," he said.