The home side dominated the possession in the first period, but could not make the breakthrough despite a number of chances.
A power cut inside the stadium delayed the start of the second half, but the action did resume despite the rain falling in Vigo.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action.
CELTA VIGO: Yoel; Mallo, Costas, Fontas, Toni; Rafinha, Oubina, Mina, Krohn-Dehli; Nolito, Charles
LEVANTE: Navas; Navarro, Juanfran, Lopez, Rodas; Diop, Simao, Xumetra; Garcia, Ivanschitz, Diawara