Barcelona's victory helped them retain their one-point advantage over Real, who kept alive their title hopes with a convincing 5-1 victory over 10-man Athletic Bilbao.
The Catalans need a win at home to lowly Real Valladolid next weekend in their last game to wrap up a second successive league title.
But Real's Chilean manager Manuel Pellegrini is refusing to admit defeat.
"We have one more match and although we had a lot of hope riding on the game in Seville, Valladolid have a lot at stake when they visit Barcelona next week. We will maintain our pressure until the end," he told a news conference.
"We knew that Barcelona's match against Sevilla would be more complicated than next week's against Valladolid, but you never know what may happen. We need to maintain this spirit and fight until the very end. Hope is the last thing we can lose.
"We closed out a great season at the Bernabeu. We won 18 of 19 matches and scored 60 goals here, which is more than three per match. We have now scored more than 100 goals. The numbers are there. We are the top scoring team."
Real will finish their first season under Pellegrini empty-handed if Barcelona defeat Valladolid.
Speculation has linked them with several renowned managers, including Inter Milan's Jose Mourinho.