Gerardo Martino's side was left frustrated Sunday evening, meaning Atletico Madrid drew level at the top of La Liga after it drew Sevilla.
Gerard Pique's header salvaged a point for La Liga leaders Barcelona in a frustrating 1-1 draw at Levante on Sunday.
Gerardo Martino's men fell short of their usual high standards at Estadio Ciudad de Valencia, with Levante producing a fine defensive display to make it five unbeaten at home in all competitions.
Barcelona, which destroyed the same opponents 7-0 on the opening day, dropped points for just the fourth time this season with a second consecutive away draw.
In a first half otherwise devoid of clear-cut chances, it was Levante that took a surprise lead when Loukas Vyntra headed home Andreas Ivanschitz's corner, before Pique equalized in almost identical circumstances from Xavi's delivery nine minutes later.
The visitors improved after the break, with Lionel Messi twice forcing Keylor Navas into smart stops, while at the other end Levante almost claimed all three points when Ivanschitz's superb 20-yard effort prompted a superb save from Victor Valdes.
The Catalan giants remain top ahead of Atletico Madrid's home match against Sevilla, while Levante move up to 11th.
Martin Montoya replaced the suspended Dani Alves at right back for Barcelona, while fullback Juanfran started his 100th league game for the hosts.
Having withstood sustained early pressure, Levante took the lead after 10 minutes when Vyntra leapt highest to head Ivanschitz's corner across Valdes.
Undeterred by the early setback, Barcelona continued to control the tempo and leveled in almost identical circumstances after 19 minutes, with Xavi's in-swinging corner headed into the far corner by Pique.
The Blaugrana were struggling to assert their usual free-flowing style as Levante's stubborn back line proved difficult for the visitors to penetrate.
It took until the 35th minute for the visitors to create another chance of note as Xavi dragged wide from the edge of the box after neat interplay between Messi and Pedro.
But the away side showed plenty of attacking intent after the break, with Pedro's 25-yard drive stinging the palms of Navas.
Messi played a one-two with Cesc Fabregas and saw his low shot saved by Navas, before Fabregas' follow-up was headed away by Juanfran to the Argentina international, who forced a superb reaction stop from the goalkeeper.
Barcelona was beginning to grow into the game and Messi once more found space in the box to have a shot blocked for a corner.
Levante twice came close to catching the Catalans on the counter-attack, as first Pedro Lopez's volley was deflected for a corner by Jordi Alba before Ruben Garcia's header from the penalty spot was well held by Valdes.
Ivanschitz's came even closer with just fewer than 15 minutes remaining when he let fly from 20 yards and was only denied by an excellent stop from Valdes.
Both sides had chances in the closing stages, with Barcelona substitute Cristian Tello testing Navas with a curling strike from the edge of the box before Garcia broke free of the defense at the other end only to shoot straight at Valdes.