Malaga beat Zaragoza 1-0 thanks to Ignacio Camacho's second-half header on Saturday, keeping the Costa del Sol side undefeated in the Spanish league despite a tumultuous off-season and the exit of several key players.
Right back Eliseu Pereira capped his strong overall performance by directing a corner kick to Camacho, who headed in from the near post in the 56th minute.
"I think we had the clearest scoring chances," said Malaga coach Manuel Pellegrini. "Eliseu had two or three clear ones and, as we expected, the match was decided on a set piece because the game lacked rhythm."
Also, Mallorca took the overnight lead of the Spanish league with a 1-0 win over Real Sociedad. Celta Vigo downed Osasuna 2-0, while Getafe drew 1-1 at Deportivo La Coruna.
Argentine forward Javier Saviola debuted for Malaga at the start of the second half after joining the club from Benfica. Malaga also brought in Roque Santa Cruz from Manchester City and American centre back Oguchi Onyewu from Sporting Lisbon late on Friday just before the transfer window closed.
The late reinforcements came after Malaga made it through the Champions League playoff round without several players it sold in the summer, including Santi Cazorla to Arsenal.
So far, the short-handed Malaga has not shown any signs of strain, displaying maximum efficiency by turning three goals into two wins and a draw in the domestic competition.
"We haven't had physical or mental problems," said Pellegrini. "I was worried our effort might slip, but the players showed that they have remained focused."
Mallorca showed more scoring intent than Sociedad throughout the match at Iberostar stadium, and its insistence paid off in the 75th when Victor Casadesus turned former Espanyol midfielder Javi Marquez's dipping cross into the net with a sharp header.
Mallorca's second home win in as many games lifted it top of the standings with seven points, ahead of Malaga on goal difference.
Celta scored twice after halftime to give the newly promoted team its first win in Spain's top flight after five seasons in the second division.
Celta tops Osasuna
At Balaidos stadium, striker Iago Aspas headed Augusto Fernandez's cross into the far corner of the net to open for Celta in the 69th, and Mario Bermejo sealed the win in stoppage time after some woeful defending by Osasuna.
Osasuna, which has lost all three matches of the season so far, was limited to Joseba Llorente's header which crashed off the crossbar in the 11th.
Osasuna coach Jose Mendilibar was at a loss to explain his team's shabby play.
"There was only one team on the pitch today, we were a shadow of our rival from the 15th minute on," said Mendilibar. "We spent a lot of time running around like headless chickens."
At Riazor stadium, Ivan "Riki" Sanchez netted for Deportivo six minutes in with a blast from outside the area. The striker took a short pass from a free kick, used one touch to open an angle around the crowded area, and unleashed a left-footed shot just inside the upright.
Abdelaziz Barrada levelled for Getafe in the 26th when the Moroccan midfielder collected a through pass and rifled by goalkeeper Daniel Aranzubia, scoring a goal reminiscent to last round's winner against Real Madrid.
On Sunday, Barcelona hosts Valencia while Madrid looks for its first win in league play against Granada. Also, Rayo Vallecano and Valladolid will try to extend their perfect starts against Sevilla and Athletic Bilbao, respectively, and Espanyol visits Levante.
Originally scheduled for Monday, Real Betis vs. Atletico Madrid has been postponed due to international matches.