Former Real Madrid midfielder Oscar, 20, struck the game's only goal to lift former Southampton boss Mauricio Pellegrino's side up three places to 11th in the table after one defeat in their last six league matches.
Levante have lost four of their last six and remain 15th, seven points above the relegation zone.
Oscar, who had struck the crossbar direct from a free-kick in the opening exchanges, fired Leganes into a 13th-minute lead.
He drilled a low angled shot into the bottom corner from the left edge of the penalty area following a swift counter-attack by the home side.
Levante created several chances as they chased a first-half equaliser and Enis Bardhi's shot hit a post shortly before the interval.
Oscar and Recio went close to doubling Leganes' lead either side of the hour-mark and Levante goalkeeper Aitor Fernandez denied the former his second goal of the game with a fine save in the closing stages.