Barcelona held by battling Levante
Barcelona's midfielder Sergio Busquets (top L) vies with Levante's defender David Navarro during the Spanish league football match Levante UD vs FC Barcelona at the Ciutat de Valencia Stadium in Valencia on January 19, 2014 - by Jose Jordan
Loukas Vyntra got the hosts off to the best possible start as he headed low past Victor Valdes from Andreas Ivanschitz's cross after 10 minutes.
Gerard Pique quickly levelled from another corner but, despite intense pressure from the visitors after the break, they couldn't find a way through.
The point moves Barca one point clear of Real Madrid and Atletico Madrid at the top of La Liga, but Atletico can go top should they beat Sevilla later on Sunday.
"We created chances but we didn't have a good day in front of goal," said Barca boss Gerardo Martino.
"I don't think we should be worried looking to the future.
"There were games at the start of the season when we won and we didn't play very well. Today is completely the opposite. We played very well and the result is a bit negative, but it is not what we deserved."
Levante had been 6-0 down at half-time on their way to a 7-0 thrashing at the Camp Nou on the opening day of the season.
However, Los Granotes made a far more positive start this time around when Vyntra headed home Ivanschitz's cross as Barca conceded from a corner for the sixth time in La Liga this season.
The lead only lasted nine minutes as the visitors levelled in similar circumstances when Pique climbed highest to head home Xavi's corner.
Thereafter, though, Barca struggled to create opportunities against Levante's back five in the first period, with Xavi's drive from the edge of the box that drifted wide their best effort from open play.
Gerardo Martino's men were more precise in their build-up play after the break and Alexis Sanchez managed to get in behind the Levante backline five minutes after the restart, but he delayed when faced with Levante keeper Keylor Navas and the chance was eventually snuffed out.
Cesc Fabregas was next to try his luck with a powerful shot from distance that was parried away by Navas.
And Navas had to be at his best five minutes later as he denied Messi after he had been played in by a neat one-two with Fabregas, before Juanfran blocked Xavi's follow-up effort on the line.
Juanfran again put his body on the line to turn another goal-bound effort from Messi behind moments later.
However, Levante were maintaining a threat on the counter-attack and Valdes had to get down to hold Ivanschitz's header from Ruben Garcia's cross.
Ivanschitz forced Valdes into another flying save 15 minutes from time as Barca left themselves exposed by pouring forward in search of a winner.
However, they came desperately close to that winner five minutes from time when Cristian Tello's curling effort was brilliantly turned behind by Navas.