The Valenciano derby ended in a stalemate, increasing the pressure on the home side, who are now without a win in four matches in all competitions
Jonas opened the scoring for the hosts midway through the first half but was pegged back by an Arouna Kone goal in the second period. Both sides had excellent chances to win the game towards the end, but poor finishing led to a share the spoils.
Los Che boss Unai Emery was deprived of leading scorer Roberto Soldado through suspension, which meant a start up front for Aritz Aduriz, while Dani Parejo was preferred in midfield over Tino Costa.
Emery had pledged a response to his side's run of three straight defeats in all competitions, but it was the visitors who made the brighter start to the game, with Jose Barkero and Kone combining well in the final third before the latter's weak attempt was easily gathered by Vicente Guaita.
The Granotes were let off the hook early on, though, when Sofiane Feghouli's cross evaded the Levante defence before finding its way to Parejo, who somehow skied his shot from close range when it seemed easier to score.
Valencia settled into their stride as the half wore on, but chances were few and far between for the hosts as their build-up play was far too laboured to seriously trouble Juan Ignacio Martinez's side.
But Emery's men managed to get the all-important first goal with a rare move of quality in what was otherwise a dire first half.
A Levante attack broke down allowing the hosts to bring the ball out quickly to Aduriz, who played a perfectly-weighted reverse-pass to Feghouli down the left, allowing the Algeria international to square the ball for Jonas to tap in to the gaping goal.
The second half began in the same vein as the first had ended, with Valencia hogging possession but struggling to create many clear-cut openings.
And they were made to pay for failing to make their superiority count as the visitors drew level against the run of play courtesy of a classic route one goal.
Los Che went to sleep defensively as Barkero played a long crossfield pass towards the back post to Valdo, who nodded across goal to allow Kone to power a finish past Guaita.
Valencia responded by injecting more urgency into their play as Jonas went close twice through long-range efforts.
The visitors were not content to settle for a point, however, as Barkero nearly played in Kone, but Guaita was alert enough to come forward and collect the ball the striker's feet.
The Ivorian then had a golden chance to clinch the three points, but fired his shot agonisingly wide of the goal from Pedro's cut back.
In a frantic finish to the game, substitute Paco Alcacer could have won it for the hosts but headed straight at Gustavo Munua from Pablo Hernandez's inviting cross as Levante deservedly held on for the point.
Valencia's next assignment sees them host AZ in the Europa League quarter-final second leg on Thursday, with the Dutch side leading 2-1 from the first leg, while Levante welcome Atletico Madrid to the Ciutat de Valencia next weekend.