Fellow title challengers Real Madrid, meanwhile, made it back-to-back wins with a thumping 6-0 victory over Espanyol in a game that saw Cristiano Ronaldo become Los Blancos' all-time leading scorer in the league.
Week Three's action began in Valencia on Friday evening as Levante welcomed out-of-form Sevilla. It proved another frustrating 90 minutes for Unai Emery's side as a 1-1 draw meant that the Europa League winners are still looking for their first three points of the season.
On Saturday, Valencia recorded their first win of the season with a 1-0 success at Sporting Gijon, while Real Betis also put their first three points on the board with a 1-0 victory at home to Real Sociedad, who have still not scored in the league this term.
Newly-promoted Las Palmas are still waiting for their first league win of the season, but Paco Herrera's side came from 3-1 behind to claim a point in a six-goal thriller at Celta Vigo, before Malaga and Eibar played out an uneventful goalless draw in the final La Liga fixture on Sunday.
Here, Sports Mole picks out its star XI from the latest round of matches.
Jaume Domenech (Valencia)
The Frenchman's training performances over the international break led to head coach Nuno throwing him in for his Valencia debut against Sporting Gijon on Saturday. It was a decision that paid dividends, with the 24-year-old making a host of excellent stops in his team's 1-0 win. Indeed, his fine display also earned the goalkeeper a new three-year contract.
David Simon (Las Palmas)
The 25-year-old has made an excellent start to life in La Liga and continued his impressive form in Las Palmas's 3-3 draw with Celta Vigo on Sunday. The full-back was part of a team that were reduced to 10 men in the 11th minute, but still managed to recover and indeed secure a point. Simon set up his side's first goal in Vigo, before scoring the equaliser 15 minutes from time.
Sevilla might not have made the best start to the new season, but they are still a team full of quality, especially in the final third. Levante had to come from behind in Friday's match to draw 1-1 with Emery's side and it was a strong defensive performance that contributed to the point. At the heart of it was Juanfran, 39, whose experience in central defence proved vital.
Ivan Ramis (Eibar)
Eibar's impressive start to the campaign – two wins and one draw from three games – has been one of the surprise stories thus far and incredibly, they have only conceded one goal. Malaga were not in the best form themselves entering Sunday's match and a strong performance from Eibar was enough to claim a point. Ramis was the star of the show at La Rosaleda.
Manu Trigueros (Villarreal)
Only Barcelona have claimed more points than Villarreal at this stage of the new season and the Yellow Submarine's latest impressive showing brought a 3-1 win at Granada on Sunday. A number of Marcelino's side impressed, but it was Trigueros that stole the show. The Spaniard opened the scoring early in the second period, before setting up his team's second two minutes after.
Raul Garcia (Athletic Bilbao)
It came as a surprise when Atletico allowed Raul Garcia to leave this summer and there is no question that the Bilbao supporters will have been rubbing their hands with delight. Just 24 minutes into his Bilbao debut on Sunday, the Spaniard got on the scoresheet in what was a 3-1 victory for the Basque side. The signing of the experienced midfielder could turn Bilbao's season.
Steven N'Zonzi (Sevilla)
It has not exactly been the start to the season that Sevilla would have wanted, with just two points gained from three league matches. There was a positive on Friday, however, with summer signing N'Zonzi finding the back of the net after returning from suspension. The Frenchman could not help his team to all three points, but he had an excellent game in the middle of the park.
Gareth Bale (Real Madrid)
Bale did not find the back of the net in Real Madrid's 6-0 win at Espanyol on Saturday, but there is no question that he played a key role in the accumulation of all three points. The Welshman won the penalty that saw Los Blancos move 2-0 ahead, while he also set up two of Ronaldo's five goals in Barcelona. The 26-year-old has started the new campaign in excellent form.
Cristiano Ronaldo (Real Madrid)
Not a particularly difficult decision to include the Portuguese in this XI. Became Real Madrid's all-time leading scorer in La Liga at the weekend with five goals in Los Blancos' 6-0 victory at Espanyol. The attacker had not scored in the first two league games of the new campaign, but returned to form in spectacular style. Espanyol simply could not live with his power and pace.
Lionel Messi (Barcelona)
The birth of his second son and a long trip back from the United States meant that Messi started Barcelona's trip to Atletico on the bench this weekend. However, as is often the case, the Argentine still decided the game for the Catalan outfit. He entered in the 60th minute and preceded to run the remainder of the game, adding his side's second in their 2-1 victory in Madrid.
Aritz Aduriz (Athletic Bilbao)
Remains one of the finest and indeed one of the most underrated strikers in La Liga. It is a surprise that the forward was not given a crack in the latest Spain squad, but he did not dwell on the omission as he struck two goals in Bilbao's 3-1 win over Getafe on Sunday. The 34-year-old opened the scoring in the sixth minute, before adding his team's third in the final 10 minutes.