Los Rojillos moved off the bottom of the table thanks to goals from Kike Sola and Nino, with Javier Camunas's 90th-minute strike for Depor a mere consolation.
The visitors are now bottom, three points from safety, while third-bottom Osasuna are a point behind Celta Vigo above them.
Sola volleyed from a Miguel Armenteros cross in the 26th minute while Nino finished just after the hour mark after a quickly-taken free-kick by Lolo.
Deportivo enjoyed possession for 52.0% of the game.
Deportivo had 17 shots, including five on target.
The most effective of Deportivo three substitutions was Nélson Oliveira, who, after replacing André Santos in the 54th minute, took two shots.
Pizzi had five shots for Deportivo, more than any of his team-mates.