Celta are second, followed by Barcelona in third after the defending champions routed Rayo Vallecano 5-2, also on Sunday.
"We think we can beat anyone.
"We can go to any ground and show that we can win because we are a solid team that works hard and is dangerous," said coach Eduardo Berizzo, whose Celta side stunned a dangerous Barcelona team 4-1 last month.
Villarreal, who entered the round in first place, fell all the way to fifth, two points off the pace.
Atletico Madrid moved into fourth on goal difference with a 2-0 win at Real Sociedad, who have just one win this season.
Deportivo La Coruna scored twice in the final minutes to fight back 2-2 with Athletic Bilbao to remain in sixth, while Getafe also eased to a 4-0 victory over 10-man Las Palmas.
AP