A point for both sides yesterday means that Atletico lead the Europa League champions by seven points with just two games remaining.
Atletico now need three points from their final two fixtures at home to Barcelona and away to Granada to guarantee third place ahead of Valencia and avoid a qualifier for the group stages in August.
The La Liga champions started brightly at the Ciutat de Valencia, but couldn't find a way past Diego Marino as Mario Mandzukic's three-month goal drought continued when the Levante 'keeper got down brilliantly to save the Croatian's header nine minutes in.
Levante did go in front just after the half-hour mark when Miranda's poor defensive header presented the ball to Ivan Lopez as his low cross left Barral with the easiest of finishes for his 13th goal of the season.
Atletico responded immediately as left-back Siqueira swept home his first goal for the club since joining from Benfica last summer from Tiago's cross.
The visitors were again the dominant side for much of the second period, but were caught out once more when another simple cross from Lopez found Uche unmarked and the ball ricocheted into the net off the Nigerian after his initial effort had been saved by Jan Oblak.