They made the best possible start after eight minutes when Mario Bermejo opened the scoring, but Deportivo were level after 29 minutes when Juan Rodriguez slotted home from inside the box.
The home side were reduced to 10 men in the second period when Gustavo Cabral was given his marching orders, but the score remained level at 1-1.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary below.
Celta Vigo: Varas; Mallo, Cabral, Lago, Arceo; Oubina, Lopez, Fernandez; Bermejo, Aspas, Krohn-Dehli
Deportivo: Aranzubia; Ze Castro, Laure, Ayoze, Marchena, Bergantinos; Dominguez, Valeron, Gama; Pizzi, Riki