Bilbao had the better chances in the first period, but neither could make the breakthrough with the scores level at the interval.
The deadlock was broken in the second half, however, as Santi Mina found the back of the net for Celta 20 minutes from time.
Read how the first leg unfolded in Sports Mole's minute-by-minute live commentary below.
CELTA VIGO: Sergio; Mallo, Costas, Cabral, Jonny; Lopez, Rafinha, Krohn-Dehli, Orellana; Nolito, Mina
ATHLETIC BILBAO: Herrerin; Iraola, San Jose, Gurpegi, Balenziaga; Muniain, Iturraspe, Rico, Herrera, Susaeta; Toquero