Negredo has been given a new lease of life under Gary Neville and the win was a confidence boost for Valencia who have yet to pick up a victory in La Liga under the former Manchester United and England defender.
The former Manchester City striker stole the ball off Diego Mainz and stroked it into the corner past Ivan Kelava after seven minutes.
Santi Mina laid the second on a plate for Rodrigo and then Mina was fouled by Uche with Negredo scoring the subsequent penalty after 62 minutes.
Negredo, who has had appendicitis and was frozen out by the former coach Nuno Espírito Santo, scored his third from the spot in the 83rd minute after he was fouled by Dória.
On Sunday Negredo missed a last night minute chance against vistors Real Madrid at the Mestalla thta would have secuireda valuable La Liga victory for his managr, Gary Neville.
However Kaylor Navas blocked it with his feet at point blank range.