Gerardo Martino's Barca, missing the injured Neymar, were well below their best in a 1-1 draw at Levante's Estadio Ciudad de Valencia.
Barcelona had thumped the same opponents 7-0 on the opening day, but fell behind on 10 minutes when Loukas Vyntra headed home Andreas Ivanschitz's corner.
The lead was short-lived, Gerard Pique meeting a delivery from Xavi to level in the 19th minute with a near carbon copy of Vyntra's effort.
Barca improved in the second half, but failed to find a winner and were almost caught out by a 20-yard effort from Ivanschitz in the closing stages.
That gave Atletico the opportunity to remove Barcelona from the top of the league for the first time since September 2012, but Diego Simeone's charges fell short in a 1-1 draw with Sevilla at Vicente Calderon.
David Villa put Atletico ahead on 18 minutes, but Ivan Rakitic levelled from the penalty spot in the 73rd minute, meaning the Croatian midfielder has now scored at Real Madrid, Barcelona and Atletico this season.
The match ended on a sour note for the visitors as Alberto Moreno was sent off in the 90th minute, but Sevilla are now unbeaten in eight league games and seventh in the table.
Villarreal moved up to fourth with a comfortable 2-0 victory over struggling Almeria.
Ikechukwu Uche's 12th goal of the season put the hosts ahead after just three minutes, and Bruno Soriano scored from the penalty spot in the closing stages to confirm the points for Marcelino Garcia Toral's men.
Getafe overcame a two-goal deficit to earn a 2-2 draw with Real Sociedad in Sunday's early game.
A double inside 16 minutes from Imanol Agirretxe put Sociedad in control, but Ciprian Marica halved the deficit shortly before the half-hour mark.
Getafe's comeback was completed on 52 minutes when Pedro Leon grabbed his sixth goal of the campaign.
The home side held on for a point despite playing the last 30 minutes with 10 men due to the dismissal of Borja.
