Sevilla shook off a heavy defeat to Barcelona in the Spanish Super Cup and a shock reverse against Braga in the Champions League play-offs to beat promoted Levante 4-1 away.
A double strike from Abdoulay Konko, an Alvaro Negredo penalty and a last-minute goal from Renato helped cancel out a 10th-minute penalty from Levante's Ruben Suarez.
Two goals from Joaquin helped Valencia to a 3-1 win at Malaga as they started a new era without Spanish World Cup winning duo David Villa and David Silva.
Valencia had to sell their prize assets to Barcelona and Manchester City respectively to help finance their crippling debts over the summer, but new signing Aritz Aduriz opened his account in the ninth minute, and Joaquin struck late on.
In the day's other game, Spain striker Fernando Llorente headed the only goal as Athletic Bilbao won 1-0 at promoted Hercules.
Sevilla recovered quickly from conceding a penalty at Levante's Ciutat de Valencia stadium, levelling two minutes later when Jesus Navas's shot rebounded into the path of Konko.
LUCKY PENALTY
They were lucky to win a penalty when Diego Perotti was brought down just outside the area in the 28th minute, and Negredo netted from the spot.
Konko finished off a well-worked move in the 62nd and Renato's diving header at the far post completed the scoring.
"This is very important. After everything bad that's gone on this was just what we needed," Negredo told Radio Marca.
Financially-troubled Valencia travelled to face a Malaga side who have just been bought by a member of the Qatari royal family.
Aduriz powered in a header from a corner but the hosts battled back and Uruguayan Sebastian Fernandez flicked in a nearpost free-kick in the 44th minute.
Joaquin broke the deadlock with a deflected shot in the 70th minute, and soon after he wrapped up the points with a volley from an Aduriz lay-off.
"We've only just started, there's still a long way to go but this was the most important step today. We wanted to win to build the confidence," Valencia coach Unai Emery told reporters.
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