Elsewhere, 10-man Levante held on to claim a share of the spoils in a home date with Real Valladolid and Malaga proved too strong for struggling Almeria.
Three first-half goals helped Barcelona to a comfortable 4-1 victory over Real Sociedad which keeps them top of the La Liga table.
Brazilian forward Neymar broke the deadlock with just five minutes on the clock, before turning provider three minutes later as he crossed for Lionel Messi to nod home.
Barca were out of sight within 23 minutes, with Sergio Busquets striding forward to lash in a third from distance.
Alberto de la Bella pulled one back for Socieded on 64 minutes, but the damage was already done and academy graduate Marc Bartra stepped off the bench to compound their misery on 77 minutes.
Atletico Madrid have also taken 18 points from their opening six games, with Osasuna edged out 2-1 on Tuesday.
Diego Costa continued his fine start to the season with another brace - which takes his goal tally to seven.
He made his match-winning impact within the space of seven first half minutes, with his first goal arriving on 18 minutes before going on to convert a pinpoint cross from Koke.
Oriol Riera handed Osasuna a lifeline three minutes before half-time, but they could not find a leveller and continue to occupy a standing inside the relegation zone.
Almeria sit just above the bottom three at present, but they remain without a win after coming unstuck 2-0 away at Malaga.
It took 69 minutes for the home side to find a way though, with Fernando Tissone's header helping to ease the tension before Francisco Portillo wrapped things up in the first minute of stoppage-time.
Levante took the lead against Real Valladolid, but were left hanging on for a 1-1 draw.
Baba Diawara rounded off a flowing breakaway with the opening goal on 35 minutes, but Valladolid were level three minutes before half-time through Javi Guerra.
They really should have been in front at the break, with Zakarya Bergdich dismissed for felling Jori Xumetra inside the box.
Andreas Ivanschitz was denied from the spot, though, and Levante's 10 men dug in for a point.