Levante went ahead in the 10th minute through Loukas Vyntra's headed goal but Barca were quickly back on level terms thanks to Gerard Pique's close-range header nine minutes later.
Levante defended in numbers after that and frustrated their visitors, who now find themselves entrenched in a three-way battle for the title with the two Madrid clubs.
The point moved Levante up into 11th place and ahead of Getafe on goal difference.
Vyntra got the home side off to the ideal start when he beat keeper Victor Valdes early in the match.
The Greece international was in the right place to meet Andreas Ivanschitz's outswinging corner to head the opening goal from the middle of the area to leave Barca stunned.
Lionel Messi tried to get the visitors back on terms moments later with a drilled shot, but his effort was blocked by Juanfran.
Pedro then tried his luck with a weak shot which was snaffled by Levante stopper Keylor Navas but Barcelona equalised with their next real attack when Pique headed in Xavi's cross from the six-yard box.
The rest of the first half was a scrappy affair with no more attempts on target, but Barca went close to taking the lead early in the second period when Cesc Fabregas' 25-yard strike was blocked by Navas.
The keeper then made a fantastic save to deny Ballon D'Or runner-up Messi twice in a double save. Messi had his first shot parried by Navas with the ball falling into the path of Xavi, whose effort was blocked by Juanfran. Messi was again on hand to try with another follow-up, but his close-range header was kept out by a brilliant save from the Levante gloveman.
The Argentina striker had another shot blocked by Juanfran just after the hour mark before Levante tried their luck at the other end, with Pedro Lopez's header caught by Valdes.
Ivanschitz then forced a good diving save from Valdes, with a powerful strike from just outside of the area as Levante tried to find a late winner of their own.
In a frantic period of stoppage time, Barca went close to scoring again through Pique in a scramble inside the box, but Levante's defence held firm as they pulled off something of a shock result in front of their home fans.