The team known as the Yellow Submarine had won four games and drawn two, including holding Real Madrid 2-2, after spending last season in the second division.
They struggled in Seville, however, and Betis forward Nosa scored the game's only goal after 36 minutes when keeper Sergio Asenjo could only parry Joan Verdu's shot and Nosa put away the loose ball.
Asenjo kept the visitors in the game with a couple of smart saves and their coach Marcelino was sent off for protesting after the referee waved away a penalty appeal in the dying minutes.
Villarreal stayed fourth in the standings with 14 points from seven games.
"I am satisfied with the team's performance, though obviously disappointed with the result," Marcelino told a news conference.
"I am proud of the fact we have had to wait until the seventh round of matches to suffer our first defeat."
Champions Barcelona and Atletico Madrid top the table with a perfect 21 points after away victories on Saturday.
Barca won 2-0 at Almeria and Atletico beat city rivals Real Madrid 1-0 at the Bernabeu with an early goal from Diego Costa. Carlo Ancelotti's Real are third with 16 points.
Adrian Colunga scored twice to lead Getafe to a 2-0 win at Espanyol, ending a run of seven successive league defeats on the road stretching back to April.
The striker broke away from his marker on to substitute Pablo Sarabia's clever pass in the 73rd minute and slotted the ball into the corner.
The same partnership produced the second goal in stoppage time as Colunga fired in at the back post.
Improving Getafe made it three wins from their last four outings and climbed to eighth with 10 points from seven games, one behind Espanyol in seventh.
Levante joined Getafe on 10 points in ninth with a 1-0 win at Osasuna, when Jordi Xumetra netted two minutes from time.
The visiting forward reacted quickest to score after Osasuna keeper Andres Fernandez parried a Papakouli Diop penalty.
Promoted Elche won their first game back in the top flight since 1989, triumphing 1-0 at Celta Vigo to climb to 16th on six points.
The Alicante-based club had been unlucky not to earn a point against Real Madrid during the week, but Javi Marquez helped ease the memory as he broke away and drilled a low shot in off the far post in the 62nd minute.