Diego Simeone's men fell behind in an open contest as Enis Bardhi struck first for Levante in the 17th minute.
Marcos Llorente's deflected strike drew Atletico level eight minutes before half-time but, following Correa's astonishing miss in the second half, the visitors were left to settle for a point.
Their advantage over rivals Real Madrid stands at six points and Atletico still have a game in hand. Simeone, however, will likely be disappointed at this missed opportunity in a season where the title is theirs for the taking.
All that came of an energetic start from Atletico was a header from Luis Suarez that looped wide and they were soon punished for sloppy play in midfield.
After Atletico lost possession just inside their own half, Jorge de Frutos surged forward and slid an excellent pass into Bardhi to slot home.
The hosts saw chances to double the lead go begging as Roger Marti fired narrowly over the crossbar and Jose Luis Morales could only produce a tame effort at the end of a well-worked attack.
And they were made to pay as Saul Niguez forced Aitor Fernandez to turn behind for a corner, from which Llorente's long-range effort was deflected past the goalkeeper by Rober Pier.
Two Fernandez saves in quick succession denied first Suarez and then Llorente to prevent Atletico completing the turnaround before half-time, though Correa should have done so shortly after the restart.
The goal was at his mercy after Fernandez made a fingertip save from Suarez, but Correa could only succeed in blazing high over the open goal.
Llorente went close to doubling his tally as Atletico ramped up the pressure, yet they failed to find the decisive goal and Levante hung on for a draw that will offer some hope to Madrid and Barcelona.
What does it mean? Atletico stretch run in underwhelming fashion
It is now 11 LaLiga games unbeaten for Atletico, but that will be cold comfort for Simeone, whose side had enough chances after going behind to claim victory and move eight points clear of Madrid.
Levante, who saw Carlos Clerc denied by Jan Oblak late on, remain comfortable in mid-table and were good value for a point.
Saul pulls the strings
The creator in chief for Atletico was undoubtedly Saul, who played five key passes during an impressive outing alongside goalscorer Llorente in midfield.
Correa can't keep it down
Correa's miss was reflective of his overall performance, with none of his three shots in his 81 minutes on the pitch hitting the target.
After making up a game in hand in Valencia, these two sides will do it all again at the Wanda Metropolitano on Saturday.