Rayo Vallecano put their miserable 6-1 defeat to Valladolid last weekend behind them to register their first win in five games with a 2-1 victory over Deportivo at Vallecas.
The hosts were 2-0 up within half an hour as Piti slotted home at the back post from Leo Baptistao's cross before Jose Carlos' drove in his first goal for the club from the edge of the area.
However, Depor were given a lifeline when Javi Fuego was adjudged to have brought down Alex Bergantinos inside the area just before half-time and Pizzi confortably converted the spot-kick.
Riki and Nelson Oliveira then had good chances to salvage a point for the visitors in the second half but neither could find the target as they slipped to a third consecutive defeat.
Rayo boss Paco Jemez resorted to a back four after coming under fire for persisting with his 3-5-2 formation throughout the game at Valladolid but it was his changes further forward that created the opener as the recalled Leo and Piti combined for the latter the sweep home his second goal of the season on 18 minutes.
Ten minutes later Rayo doubled their advantage as Andrija Delibasic pulled the ball back for Jose Carlos and his strike took a slight deflection off Ze Castro to leave Depor goalkeeper Daniel Aranzubia with no chance.
Deportivo had hardly threatened at all in the first half but were given the opportunity to get themselves back into the game when Fuego was harshly penalised for his challenge on Bergantinos - but Pizzi had no sympathy for the hosts as he smashed his penalty straight down the middle of the goal.
After a quiet opening to the second half both sides had a number of chances in the final half hour.
Delibasic was first to threaten but he overran the ball when clean through on Aranzubia and allowed the keeper to clear, while at the other end only a fantastic block by Tito denied Oliveira's initial effort before the Portuguese international pulled his follow-up attempt wide.
Jose Carlos was next to fail in front of goal as he unsuccessfully tried to round Aranzubia when a simple pass to Nicke Bille would have left the Dane with an open goal and that carelessness could have cost Rayo as Riki was played through on goal by Bergantinos with two minutes to go - but the ball took a bobble as the striker took aim and his effort trickled wide.