Promoted Cadiz scored two goals in three minutes as the surprise packages beat hosts Eibar 2-0 to join Real Sociedad at the top of the La Liga table.
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Goals from Alvaro Negredo in the 36th minute and Salvador Sanchez Ponce three minutes later put the visitors on 14 points from eight games, with Sociedad ahead on goal difference and with a game in hand at Celta Vigo on Sunday.
"The league lead? It means we are close to our objective (of avoiding relegation). We can't think beyond that," Negredo said.
"These points are great to have now because we know that bad stretches will come."
Real Madrid, who host Huesca on Saturday, are a point behind in third and have played two games fewer than Cadiz.
Cadiz have already caused a stir this season, notching a shock 1-0 win at Real Madrid earlier this month.
Coached by Alvaro Cervera, the team has climbed from the third division in 2015-16 to making a remarkable return to the top-flight with a side featuring veteran players doing their best to prolong their careers.
Besides former Sevilla and Manchester City striker Negredo, the squad includes former Atletico Madrid midfielder Augusto Fernandez and veterans Alex Fernandez, Juan Cala and Jose Martin.
"Once we get ahead, we are tough to beat," Negredo said. "We defend very well."
Australian Associated Press