The result marks Joaquin Caparros' side's fourth straight La Liga defeat, with Pedro Leon striking with 11 minutes remaining to secure Getafe's first win in three.
Luis Garcia's men - who were hammered 7-0 at Atletico Madrid last time out - controlled the majority of the game, with Diego Castro and Ciprian Marica both seeing efforts on goal blocked before Leon broke the deadlock.
The victory lifts Getafe up to sixth the table, and stretches 13th-placed Levante's winless Liga streak to five matches.
In Friday's other Liga fixture, fourth-placed Villarreal missed the chance to move within four points of Real Madrid in third as Weligton's injury-time equaliser gave Malaga a 1-1 draw at El Madrigal.
Marcelino's side went ahead just after the half-hour mark as Bruno scored his fourth goal of the campaign with a neat finish, and Giovani dos Santos almost made the points safe when he drew a fine save from Willy Caballero a minute from time.
However, captain Weligton earned his side a share of the spoils with a 94th-minute header.