A Sunday of away wins in the Spanish Liga saw Valencia keep top spot ahead of Sevilla and Real Madrid, while defending champions Barcelona moved up to joint fourth despite star striker Lionel Messi being stretchered off injured, dpa reported.
Messi scored Barca's first goal in their 2-1 win away to Atletico Madrid but suffered a badly twisted right ankle at the end and will be out of action for at least two weeks.
Valencia, who won 2-1 away to Hercules despite the sending-off of captain David Navarro, are the only team to have won all three of their matches.
Juan Mata and Pablo scored early goals for Valencia, but David Trezeguet pulled a goal back for the hosts for the penalty spot - then came close to making it 2-2.
"We really suffered in the second half," said Valencia winger Joaquin.
"The expulsion of Navarro was not fair," he added. "It was difficult to play with one man less for most of the second half. It is a win with a lot of merit, in the circumstances."
Mata, a reserve for Spain at the World Cup, gave Valencia the lead after just two minutes with a spectacular volley to a Pablo centre.
In the 23rd minute Mata returned the compliment and set up Pablo to make it 2-0 with a right-foot drive into the top corner.
Two minutes before half-time Navarro handled for a clear penalty, which was calmly converted by Hercules' star signing Trezeguet.
Five minutes into the second half Navarro was harshly given a second yellow card for an alleged foul on Abel Aguilar, and Valencia suddenly had their backs to the wall.
As Hercules piled on the pressure, Trezeguet headed against the post and ageless keeper Cesar was forced to pull off several sharp saves as Valencia clung on for a tight win.
Valencia are two points ahead of Sevilla and Real Madrid, having made their best start for more than 20 years.
Sevilla came from behind to win 2-1 away to Malaga in Sunday's late match, with goals from Alejandro Alfaro and Martin Caceres.
"It was lovely to score my first goal (for Sevilla)," said Caceres, "especially as it turned out to be the winning goal."
The Uruguayan World Cup defender added that "Malaga are a good team, but i think we were just a little bit better than them today."
Jose Rondon gave Malaga the lead in the 14th minute after the Sevilla defence had failed to clear a corner, only for Alfaro to quickly make it 1-1 with his head after a good centre from Diego Perotti.
Caceres made it 2-1 for Sevilla just before half-time by heading in a free-kick from Tiberio Guarente.
Malaga never threatened to force a draw in the second half and Sevilla should really have won by a bigger margin.
Sevilla are now level on seven points with Real Madrid, who battled out a streaky 2-1 win away to luckless Real Sociedad on Saturday.
In joint fourth place, on six points, are four teams: Atletico Madrid, Villarreal, Barcelona and Espanyol.
Barca scored a valuable 2-1 win away to an Atletico Madrid side that had beaten them in their last three visits to the Estadio Calderon.
Barca won with goals from Lionel Messi and Gerard Pique - and despite an astonishing display from Atletico's teenage goalkeeper David de Gea.
The bad news for Barca was the late injury to Messi, for which Atletico defender Tomas Ujfalusi was sent off.
Barca coach Josep Guardiola said, "We are happy because of the win but sad because of Leo's injury."
Guardiola added: "I am very proud of my team. The three points are the consequence of our performance, against good opponents...I really cannot ask for more. This gives me faith and confidence in the future."
He finished by praising De Gea for "a memorable performance."
Barca, playing in an unusual green away strip, dominated most phases of the match and would have won by a greater margin had it not been for De Gea.
In the 13th minute David Villa hit De Gea's post, only for the attack to continue and for Messi to make it 1-0 with his trusty left foot after being played through by Pedro.
12 minutes later Raul Garcia equalized for Atletico, against the run of play, by heading in a corner that Barca keeper Victor Valdes made a mess of.
But in the 33rd minute Pique restored Barca's lead with a low right-foot drive, after having skilfully controlled a corner on his chest and skipped round sluggish defender Diego Godin.
Villa, Messi and Pedro were all foiled by De Gea in the second half, as the Catalans looked to bury Atletico with a third goal. But that made little difference because the hosts failed to create clear chances to equalize.
At the end Atletico right-back Tomas Ujfalusi was sent off for pulling down the rampant Messi.
Villarreal, meanwhile, were moving up to joint fourth with a 2-1 win away to bottom team Levante, who have lost all three of their games. Villarreal's hero was Brazilian striker Nilmar, who struck in the 16th and 43rd minutes.
Felipe Caicedo pulled a late goal back for Levante, but Villarreal had few problems in holding out for an important win.
Sunday's other early game saw Racing Santander score their first win, 2-0 at home to Zaragoza thanks to late goals from Henrique and Ariel Nahuelpan.
The win takes Santander up to sixth from bottom and pulls Zaragoza, who have just one point, down to second from bottom.
The third round of matches will finish on Monday with Deportivo Coruna at home to Getafe.