Nolito scored the only goal of the game after 19 minutes and Celta were fortunate not to lose their lead in the second half, with Levante's David Barral missing a penalty and then having a shot blocked on the goalline by Celta goalkeeper Yoel Rodriguez, which looked as if it may have crossed the line.
The result sees Celta move onto 33 points, just three behind Levante, whose European ambitions were dealt a blow by the defeat.
The hosts started the game well, Andreas Ivanschitz forcing an early save from Yoel from a free-kick, and then Barral heading just over the bar at the near post.
Match winner Nolito looked the most dangerous player for Celta, having their first real chance of the game with a quarter of an hour played, combining with Charles before shooting just wide of the post.
The forward did not have to wait much longer before finding the net, however, arriving at the far post to slam in a square pass from Augusto Fernandez.
And Nolito could have made it 2-0 just a few minutes later, striking the post with a diagonal shot.
The highlight of the game arrived 15 minutes into the second half, when both teams could have scored within quick succession.
Levante stopper Keylor Navas further cemented his reputation as the most in-form goalkeeper in the league by repelling a volley from Nolito with his legs, and kept the ball in play, allowing Levante to counter.
The hosts moved the ball quickly on the break, leading to Victor Casadesus running into the box and getting his legs swiped by Celta full-back Jonny.
Levante's players and coach Joaquin Caparros were furious that the referee only showed a yellow card to the offending Jonny, and then Barral was forced to wait to take the penalty.
Perhaps the tension went to the striker's head, as he blasted the ball off the crossbar.
Barral then had another chance to equalise, but could only shoot straight at Yoel from close range, the goalkeeper struggling to prevent the ball from going over the line, but just about succeeding - according to the referee's judgement.
Michael Krohn-Dehli could have wrapped up the points for Celta on the break, but saw his shot blocked after Fabian Orellana had cut the ball back to him, and at the other end Barral and Ivanschitz were both denied by the excellent Yoel.
Celta substitute Santi Mina was unable to grab a second goal for the visitors in injury time, failing to keep his shot under the bar, but the final whistle blew just moments later, announcing that the three points belonged to the Galicians.