Negredo netted twice for the home side after Fazio had powered home Antonio Luna's corner from close range for the opening goal on 11 minutes.
Negredo darted onto a lovely ball from Manu to slip the ball beyond the visiting keeper Roberto Gago on 29 minutes as Sevilla set about their business with some relish.
He headed Sevilla's third goal of the evening beyond Gago two minutes before the break from a Jesus Navas cross after the Real Zaragoza keeper had saved his initial shot.
Sevilla could have won by more against a visiting side who could not really cope with the movement of Negredo and Navas.
Sevilla retain outside notions of qualifying for the Champions League. They remain in seventh place, but are only five points behind fourth-placed Malaga who slumped to a 2-1 defeat at Villarreal earlier in the evening.
Zaragoza seem destined for relegation with fourth-bottom Villarreal seven points clear of La Liga's second-bottom team on 35 points with Zaragoza and Sporting Gijon on 28 points.