The two teams were promoted last season but are in serious peril of going straight back down.
Depor have 20 points from 28 matches while second from bottom Celta, who have lost six of their last seven games, are on 23, one point behind Real Mallorca who visit second-placed Real Madrid on Saturday.
Forward Riki fired the home team ahead in the ninth minute at the Riazor when he controlled a Juan Carlos Valeron pass with his thigh and volleyed brilliantly past keeper Javi Varas.
Celta were reduced to 10 men in the 29th minute when striker Iago Aspas was shown a straight red card for butting Depor defender Carlos Marchena in the face.
Silvio made it 2-0 in the 64th minute with a stunning long-range volley and substitute Diogo Salomao added a third goal 14 minutes later, moments after replacing Riki.
South Korean forward Park Chu-young pulled a goal back for Celta 10 minutes from time but it did little to dampen the enthusiasm of the home support celebrating a morale-boosting success against their bitter local rivals.
"It was a very important match for us and there was a lot at stake because of the situation we are in, the opponent, and everything else," Valeron told Marca TV.
"We are very happy with the win and for giving our fans a bit of joy during such a difficult time," he added after Depor recorded their fourth league victory of the season.
"Our task is a very tough one but I think this will give us a lot of strength and let's see if things will go a bit better from now on. It's a very small step and there is still a long way to go."
Leaders Barcelona seek to protect their 13-point advantage over champions Real when they host eighth-placed Rayo Vallecano on Sunday.
Celta Vigo enjoyed possession for 48.1% of the game.
Celta Vigo had 10 shots, including one on target.
The most effective of Celta Vigo's three substitutions was Chu-Young, who, after replacing Mario Bermejo in the 69th minute, scored one goal.
Bermejo had three shots for Celta Vigo, more than any of his team-mates.