Athletic Bilbao got their first points on the board of the Liga season with a 3-1 home win over Getafe that featured a debut goal from Raul Garcia.
Aritz Aduriz nodded home after just six minutes before the former Atletico Madrid midfielder headed high into the net following Markel Susaeta's cross midway through the first half.
Emiliano Vazquez's fine finish after 70 minutes gave Getafe hope but Aduriz scored his second with seven minutes to play to earn Athletic their first win of the Liga campaign.
Villarreal were also 3-1 winners in their visit to Granada, with two goals in two second-half minutes setting up their second victory of the season.
Manu Trigueros' pinpoint strike got the visitors on their way before he teed up Cedric Bakambu to add a quickfire second.
Fran Rico got a goal back for Granada but Samuel made sure of the points in stoppage time with a clever finish from a tight angle.
Las Palmas recovered from the early sending-off of goalkeeper Javi Varas to snatch a point in a six-goal thriller against Celta Vigo.
Varas was dismissed after bringing down Iago Aspas after just 11 minutes, with Fabian Orellana converting the resulting penalty and Daniel Wass adding a second five minutes later.
Sergio Araujo halved the deficit before Nolito drilled in Iago Aspas' set-up to put Celta in control of the game.
But Araujo turned home Antolin Alcaraz's header on 61 minutes and Las Palmas completed an unlikely comeback when David Simon finished following Juan Emmanuel Culio's pass.
Malaga, meanwhile, are still waiting for their first Liga win of the season, after being held to a 0-0 draw by Eibar, who stay fifth.