Ten-man Valencia almost sealed a draw from a two-goal deficit but lost 3-2 in the 93rd minute against Real Betis on Sunday.
Ruben Castro struck in the first half before Joaquin doubled the lead shortly after Enzo Perez had been sent off. But the blow did not stop Valencia's comeback as they hit two goals in three minutes from Rodrigo and new signing Ezequiel Garay.
However, Castro struck again with only seconds to spare to take all three points and condemn Valencia to defeat. Los Che have now lost their last six La Liga games, their worst ever run in the competition.
Sporting Gijon will spend the week sitting ahead of champions Barcelona in La Liga following a 2-1 win over top-flight new boys Leganes at El Molinon.
Nacho Cases profited from some poor defending and Duje Cop netted a penalty before half-time to pave the way for a second successive home win to start the season. Diego Rico pulled a goal back for Leganes after half-time, but the Madrid club slipped to their first-ever defeat in Spain's top flight.
Athletic Bilbao got their first points of the campaign as a Raul Garcia piledriver proved to be enough to settle a low-quality encounter away to Deportivo La Coruna.
Ernesto Valverde's men were lucky to claim a 1-0 win though after Depor incorrectly had a late equaliser ruled out for offside against Florin Andone, who was being played on by Oscar de Marcos before blasting in his shot with five minutes to go.
A last-gasp winner from Sergi Enrich maintained Eibar's positive start to the season as they secured a 2-1 victory away to Granada.
The Basque side, who had beaten Valencia prior to the international break, had goalkeeper Asier Riesgo sent off for a foul on Granada's Ezequiel Ponce after half an hour but still headed into the interval in front thanks to Pedro Leon's long-range strike.
Granada's Dynamo Kiev loanee Artem Kravets deservedly grabbed the equaliser with 15 minutes to go but Eibar snatched it with a stoppage-time strike from Enrich.