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 Ligathis season.
The lead only lasted nine minutes as the visitors levelled in similar circumstances when Pique climbed highest to head home Xavi's corner.


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