Mallorca could have gone top of the table with a victory but Sevilla were a cut above and took the spoils thanks to first half goals from Sebastian Squillaci and Argentine Diego Perotti.
Sevilla welcomed back Brazilian international Luis Fabiano but it was French centre-back Squillaci who surprisingly opened the scoring after 17 minutes.
It was a goal made in France with Julien Escude heading the ball across goal for compatriot Squillaci to head in off the underside of the crossbar.
The second goal was created brilliantly by Fabiano and Jesus Navas who crossed for Perotti to head home from close range.
Mallorca had a golden chance to make it 2-1 close to half-time but Fernando Varela was foiled by Andres Palop.
Brazilian Adriano almost made it 3-0 minutes after the interval but a last-ditch block denied him a brilliant solo goal.
Sevilla climb to third with their third consecutive victory while Mallorca lie sixth after their first defeat of the campaign.
Champions Barcelona can replace Real Madrid, ahead on goal difference, at the summit with a draw or win at Racing Santander at on Tuesday.
Barca have a perfect nine points but historically Racing has not been a happy hunting ground and they have only won 13 out of their 41 visits to El Sardinero.
"It has been a complicated ground for us and a lot of other teams," said Barca coach Pepe Guardiola. "We have done well against them recently but always by a narrow margin."
If Barca defeat Racing it will be the first time since 1997/98 that they have started a season with four straight wins.
Real Madrid?s expensive 'Galacticos' face their hardest test so far with a trip to Villarreal on Wednesday as coach Manuel Pellegrini goes back to his old club.
"It is a joy to go back to Villarreal," said Pellegrini. "They were five years at a great club and I met some fantastic people. The fans always treated me well during my time there and I hope I get a good reception."
Pellegrini has guided Real to three straight victories while his successor at Villarreal Ernesto Valverde has yet to win a game.
Atletico Madrid, another team pushing for a top four spot, have also had a nervy start with just one point from nine ahead of Wednesday's home match against Almeria.
Coach Abel Resino got the dreaded vote of confidence from Atletico president Enrique Cerezo this week following the 5-2 humiliation by Barcelona over the weekend.