In a scrappy affair that boasted 10 bookings and a sending off, hosts Celta took the lead when Mario Bermejo scrambled home from close range after Iago Apsas beat a terrible Depor offside trap.
The visitors drew level when Juan Dominguez finished off Juan Carlos Valeron's marvellous through-ball just before the half hour, replays inconclusive as to whether the goal-scorer was onside.
Home defender Gustavo Cabral was shown two bookings in two minutes early in the second half, but the visitors could not exploit their man advantage and Celta looked the more threatening in the latter stages.
Depor stay in the bottom three, while Celta lie in mid table.
It was the 118th Galician derby but the first in the top flight for five years.