Levante went ahead in the 17th minute against the run of play after their group pressing helped win the ball and Jorge de Frutos accelerated down the pitch before he passed to Enis Bardhi who pulled off a composed finish.
The game, postponed from the start of the season, offered Atletico the chance to peel further away from nearest challengers Real Madrid but a second draw in three games only moved them on to 55 points.
They are still in the driving seat for a first title since 2014, however, leading Real by six points and with a game in hand. Barca are third on 46.
"We don't look at the points difference, we've gained a point today and we don't care about the gap, we'll just keep focusing on winning each game," said Atletico keeper Jan Oblak.
"We played well but a defensive error cost us a goal. They didn't have many chances after that and we missed really clear chances and it was down to bad luck that we didn't win."
Levante are down in 11th but they have a strong record against the top sides and pulled off a shock 2-1 win at Real last month.
"We faced a tough opponent who are playing well. They've improved in defence and they bring the ball out well. They ended up scoring with their first chance," said Atletico manager Diego Simeone.
"The team worked hard to equalise, winning corners, creating chances, and we got the equaliser. Then in the second half we did well, we had clear chances and in the end we could have lost with Levante's chance. It was a fair draw."
Atletico should have taken the lead soon after the interval when Angel Correa blasted way over the bar when the ball landed at his feet inside the area.
Llorente came close with another distance strike which fizzed past the post while Levante keeper Aitor Fernandez kept out efforts from the league's top scorer Luis Suarez and midfielder Saul Niguez, who also had a late goal ruled offside.
But Simeone's side were fortunate in the end to take a point from the game as it took a top-draw save from Oblak to prevent a volley from Levante's Carlos Clerc creeping into the net in the closing stages.
The two sides meet again on Saturday at Atletico's Wanda Metropolitano stadium.