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.
"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."
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.
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.
