Fermin Lopez scored before being sent off in the second-half. Robert Lewandowski, Raphinha and Eric Garcia also struck for the visitors. Ruben Vargas struck for Sevilla to cancel Lewandowski's opener.
Afterwards, Flick declared himself satisfied with the result and the efforts of his players.
The match:
"I would like to highlight our game. In the first half we played well, it was a good match, and in the second we fought and changed things. We played quickly, we changed positions... Fermin's goal helped us, and then Raphinha's. I am proud of the team, the red card was a great test and we scored. I am very happy.
"We don't care about others, I've already said that. We have to do our job. We have to focus on ourselves and not think about others."
Gavi and Fermin:
"They have potential and I'm happy with their intensity. Sometimes these things happen. You have to accept it. I see that the team improves in these situations.
"We defended well. They have good, fast players on the wings and we defended very well. We were patient."
Ronald Araujo:
"We expect a test tomorrow and we hope it's not too serious. That's what it looks like."
Fermin Lopez:
"He scores an important goal and then gets sent off... it's intense. These things happen. It's a good lesson for the future."
Feelings:
"I'm happy because we won, it's three important points. It's a long road. It helps us. We have to keep this mentality. We'll have three days off to recover, the team deserves it. Then on Thursday we'll start preparing for the next match.
"We didn't prepare well for today's game because we played on Thursday. And look, we won. A week without a game doesn't guarantee you anything. But we have more time to rest, and that's good."
Ansu Fati:
"I've been honest with him. I've spoken to him. Not everything is perfect on one day, but he's close to the team. It's important. I've seen him at the highest level and that's the level I want him to be at. It's not an easy road, but he's getting closer to returning to the team."
Pedri:
"He's incredible. He helps us a lot with the ball, he gets out of the opponent's pressure... he does it very well. I'm very happy that he played the whole game."