Despite two goals from Franco Vazquez, Sevilla's defeat leaves them on 68 points, three behind third-placed Atletico Madrid, but now only five clear of fifth-placed Villarreal — and they still have to visit Real Madrid on May 14.
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Vazquez opened the scoring at La Rosaleda in the 30th minute after breaking through from midfield, before playmaker Pablo Fornals equalised for the hosts eight minutes later with a rocket from outside the area.
Sandro Ramirez put Malaga ahead early in the second half but Vazquez levelled in the 57th minute of a fiercely contested clash after latching on to a loose ball in the box.
Malaga moved back ahead in the 77th when Diego Llorente planted a header into the top corner before substitute Juankar added the decisive fourth, snapping up the rebound after Sandro's late penalty was saved.
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Llorente, whose goal helped move Malaga up to 12th, said: "[The ball] just came to me and I took it well. It's good to get a big win like this in front of our home fans."
Sevilla midfielder Vazquez added: "We only have ourselves to blame. We made mistakes that you cannot make."
Sampaoli's side have slumped after being eliminated from the Champions League and if their bad form continues into their final three matches then Fran Escriba's Villarreal could yet take advantage.
Villarreal, though, face Barcelona at the Nou Camp on Saturday before their potentially winnable games against Deportivo La Coruna and Valencia.
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