The 27-year-old bagged a double in the victory on Monday, in a result that helps Sevilla's chances of playing in the Europa League next season
The hosts went ahead in the fourth minute when Negredo rose highest to nod home Ivan Rakitic's free-kick.
Despite the early goal, both sides settled, and it was not until the 55th minute that Carlos Gurpegi added parity to the scoreline when his flicked-header from Ibai Gomez's free-kick deceieved Beto in the Sevilla goal.
The visitors were handed fresh impetus in their pursuit of a winner when Fernando Navarro was shown a second yellow card for a foul on Aritz Aduriz.
Bilbao failed to capitalise on their numerical advantage however and it was soon 10 against 10 when Aymeric Laporte got himself booked twice in three minutes and followed Navarro down the tunnel.
Despite little time remaining on the clock, a late twist saw Negredo strike to claim all three points for Sevilla, tapping home from close range after Jose Antonio Reyes fired across the face of goal.
Unai Emery's men now move to within six points of seventh-placed Real Betis, who occupy the third and final Europa League place.
However, Sevilla have the opportunity to bridge that gap to just four points when they take on Pepe Mel's side at the Benito Villamarin this Friday.