Marcus Acuna scored a 70th minute goal which decided the contest as fourth-placed Sevilla closed the gap on the top three.
Atletico Madrid held a four-point lead at the summit heading into the weekend’s fixtures, but Real Madrid won 2-0 over Eibar to move into second, three points behind Atleti.
Barcelona, who started the weekend in second, play Valladolid on Monday and will move within one point of Atleti with victory.
Atletico have now dropped points in three of their past five games as their lead continues to be whittled away.
“I know the way and I’m not afraid of anything,” Atletico boss Diego Simeone said.
“This isn’t happening because of nerves. Being able to play better, being a strong unit, I don’t think it’s down to nerves.”
Atletico can get back on track with a good run of fixtures against Real Betis, Eibar and Huesca.
“We have to keep working and up the intensity, that’s what gave us more of a chance aside from talent,” Simeone said.
“We’ll look to do it this week, although there are some players who won’t be able to play against Real Betis. We’ll carry on preparing for the game. I’m not budging on anything, but we have to accept we’re in bad form.
“The Spanish league is tough until the end in every title race. There are usually only two teams [competing], as well as us in 2014 or 2017, but it was always a two-horse race. Now we’re competing, more for bad than for good in recent times.”