The victory at their Sanchez Pizjuan stadium lifted the Andalusian club to fifth on 45 points, two ahead of Espanyol who were beaten 2-1 at home by Racing Santander.
Perotti put Sevilla ahead in the 43rd minute when he stroked a cross from Spain winger Jesus Navas past his Argentine compatriot Leo Franco in the Zaragoza goal.
Czech midfielder Jiri Jarosik levelled four minutes later before Mali international Kanoute and his strike partner Negredo (pictured) scored from the spot in the second half.
Sevilla now have their eye on reeling in fourth-placed Villarreal and a place in Champions League qualifying, coach Gregoria Manzano said.
"Today's step is the start of the ascent we want to make," he told a news conference.
"At least we are seeing a team that has a dream and we will maintain it to the end," he added. "But we are the ones who cannot afford to slip up."
Atletico Madrid boosted their bid for European football next season when Diego Costa scored a hat-trick in a 3-2 comeback win at Osasuna in the late kick-off.
Kike Sola fired the home side ahead just after the half hour before Brazilian striker Costa struck once before the break and twice in four second-half minutes.
Javad Nekounam pulled a goal back with a penalty 10 minutes from time after Atletico winger Jose Antonio Reyes had missed from the spot and Osasuna defender Sergio Fernandez was sent off for an elbow on Costa.
Europa League champions Atletico stayed in eighth on 42 points, level with Athletic Bilbao, who play at bottom side Almeria on Monday.
HUGE SETBACK
In Saturday's games, Real Madrid's chances of ending Barcelona's two-year reign as champions suffered a huge setback when they slumped to a shock 1-0 defeat at home to Sporting Gijon and Barca won 1-0 at Villarreal.
Real's failure spoiled their perfect home record which had read 14 wins in 14 this season and ended coach Jose Mourinho's nine-year unbeaten run in home league games with Porto, Chelsea, Inter Milan and Real.
Barca have 81 points from 30 games, eight ahead of Real on 73 with eight matches left.
At the other end of the table, Malaga's troubled season took a turn for the worse when they lost 3-1 at Levante on Sunday.
Manuel Pellegrini's side remained mired in the relegation places in 19th, three ahead of bottom side Almeria, who host Athletic Bilbao on Monday.
Deportivo La Coruna beat visiting Real Mallorca 2-1 and Royston Drenthe scored twice as Hercules won 3-1 at Real Sociedad.
