Sergio Escudero scored 26 seconds into the match as Sevilla defeated Atletico 3-1 at home on Tuesday to advance to the Copa del Rey semifinals 5-2 on aggregate on Tuesday.
Atletico entered the match needing to score at least two goals to overcome the 2-1 home loss in the first leg in Madrid. But Sevilla struck in its first attack, with Escudero scoring from a shot inside the area after a well-placed cross by Sarabia.
Atletico didn't take long to equalise, with Antoine Griezmann's long-range shot going over goalkeeper Sergio Rico in the 13th minute.
But Sevilla netted again early in the second half with a penalty kick converted by Ever Banega, and Sarabia increased the lead with a low strike into the far corner in the 79th minute to seal the team's spot in the last four.
Atletico manager Diego Simeone was sent off shortly after Sevilla's final goal for complaining with the officiating crew as the result extended Atletico's winless streak to three matches in all competitions.
After already being eliminated from the Champions League, Atletico's hopes for a title this season are reduced to La Liga and the Europa League. They trail Barcelona by 11 points at the start of the league's second half.
Sevilla reached their second semifinal appearance in three years after another reassuring result for Sevilla under new coach Vincenzo Montella, who revamped the team since replacing Eduardo Berizzo late last year.
After a slow start, Montella has led Sevilla to three straight wins, putting the team back in contention for a Champions League spot in the Spanish league.
Sevilla made it to the Copa del Rey final two years ago, losing to Barcelona. They won the last of their five Copa titles in 2010.