Elche beat Celta Vigo 1-0 thanks to midfielder Javi Marquez's solo effort to claim its first win in Spain's top flight in 25 years on Sunday.
Also, Real Betis dealt Villarreal its first loss this season with a 1-0 home win, Levante 's late goal gave it a 1-0 victory at Osasuna , and Getafe striker Adrian Colunga scored twice as it beat Espanyol 2-0.
While neither team shone at Celta's Balaidos Stadium, Elche went close through Manuel del Moral's high strike just before the halftime whistle.
Marquez then broke the deadlock on a counterattack in the 62nd minute. His low shot from an angle while on the run sent the ball in off the far post.
Elche earned promotion last season, making its long-awaited return to the first division where it had gone winless through six rounds to start this campaign.
''My team deserved this win,'' said Elche coach Francisco Escriba. ''In this league there are 10-12 teams on a very similar level and it's strange that games between them are decided in another way. The sensation I have is that my team is playing well.''
Betis got its second win of the season from a combination of midfielder Emmanuel ''Nosa'' Igiebor's 36th-minute winner and some dogged defending that stifled Villarreal's previously potent attack.
Nosa charged in to hammer home a rebound off a shot by Joan Verdu that had been parried by goalie Sergio Asenjo.
''It's a shame we couldn't get something from the times when we broke into their area,'' Villarreal coach Marcelino Garcia said. ''I'm satisfied with my team's effort, annoyed by the result, but to lose your first game in the seventh round... There are different ways to lose and losing this way hurts less.''
Villarreal's first defeat left it in fourth place, two points behind Real Madrid in third. Barcelona and Atletico Madrid are another five points ahead at the top of the standings.
Levante looked ready to settle for a draw in Pamplona when midfielder Jordi Xumetra netted in the 87th following a penalty. Osasuna goalkeeper Andres Fernandez blocked Papakouly Diop's spot kick, but Xumetra raced in to slot home the rebound.
Osasuna dominated the first half but failed to capitalize, with striker Oriol Riera squandering two good chances.
Levante improved in the second half with Simao Mate's header finding the crossbar before Osasuna's Jordan Loties fouled Ruben Garcia in the area with three minutes to play.
Osasuna finished with 10 men when Alvaro Cejudo received a second yellow card in injury time.
Under new coach Joaquin Caparros, Levante has two wins, four draws and only one loss to start the season. Osasuna was left with one win and six losses.
''It was a wide-open game, and we both had clear chances,'' said Xumetra. ''But we took the points at the end from a penalty that we were lucky enough to put in.''
Colunga opened the scoring at Espanyol in the 73rd minute for Getafe when he took substitute Pablo Sarabia's throughball and fired it past goalkeeper Kiko Casillas into the corner of the net.
Espanyol searched for the equalizer but could not convert its 14 corners, Joan Capdevila and Hector Moreno going the closest with headers.
Colunga added his second goal in stoppage time to seal Getafe's first away win of the season.
It was Getafe's third win in four matches, while Espanyol has now lost two straight after starting the season unbeaten in its first five games.
''A miscue cost us the first goal and later arrived the nerves, the desperation and the heroics,'' said Espanyol manager Javier Aguirre. ''We lacked clarity. The 2-0 is too much of a punishment, but we can't let it bring us down.''