Luciano Vietto opened the scoring for the hosts in the 25th minute with a low finish and the Argentine striker tapped in a second three minutes later.
Wissam Ben Yedder fired home in the 34th minute and, two minutes later, Vitolo's close-range goal made it 4-0.
Sevilla defender Adil Rami was sent off just after the hour mark before Sandro Ramirez netted Malaga's consolation.
The victory helped Sevilla to close the gap on La Liga leaders Real Madrid, who are away at the Club World Cup in Japan, to four points.
Barcelona will overtake Sevilla with victory over city rivals Espanyol in their clash at the Nou Camp on Sunday.
Elsewhere on Saturday, Saul Niguez scored the only goal of the game as Atletico Madrid clinched a hard-fought 1-0 win over Las Palmas.
Villarreal remain in fourth spot after their 3-1 win over Sporting Gijon. They are ahead of Real Sociedad, who beat Granada 2-0 away from home, on goal difference.
Match ends, Sevilla 4, Málaga 1.
Second Half ends, Sevilla 4, Málaga 1.
Offside, Sevilla. Steven N'Zonzi tries a through ball, but Vitolo is caught offside.
Mikel Villanueva (Málaga) is shown the yellow card for a bad foul.
Luciano Vietto (Sevilla) wins a free kick in the defensive half.
Foul by Mikel Villanueva (Málaga).
Attempt blocked. Pablo Fornals (Málaga) left footed shot from outside the box is blocked. Assisted by Javi Ontiveros.
Attempt missed. Gonzalo Castro (Málaga) right footed shot from the right side of the box is high and wide to the right. Assisted by Pablo Fornals.
Foul by Pablo Sarabia (Sevilla).
Roberto Rosales (Málaga) wins a free kick on the right wing.
Vitolo (Sevilla) wins a free kick in the defensive half.
Foul by Recio (Málaga).
Foul by Timothée Kolodziejczak (Sevilla).
Pablo Fornals (Málaga) wins a free kick on the right wing.
Attempt missed. Pablo Sarabia (Sevilla) left footed shot from the left side of the box is close, but misses to the left. Assisted by Luciano Vietto.
Attempt missed. Recio (Málaga) right footed shot from outside the box is high and wide to the right. Assisted by Javi Ontiveros.
Attempt missed. Pablo Fornals (Málaga) right footed shot from more than 35 yards misses to the left.
Roberto Rosales (Málaga) is shown the yellow card for a bad foul.
Pablo Sarabia (Sevilla) wins a free kick in the defensive half.
Foul by Roberto Rosales (Málaga).
Attempt missed. Javi Ontiveros (Málaga) right footed shot from outside the box is just a bit too high. Assisted by Roberto Rosales.
Pablo Sarabia (Sevilla) wins a free kick in the defensive half.
Foul by Miguel Torres (Málaga).
Corner,  Málaga. Conceded by Matías Kranevitter.
Offside, Sevilla. Steven N'Zonzi tries a through ball, but Luciano Vietto is caught offside.
Offside, Málaga. Roberto Rosales tries a through ball, but Sandro Ramírez is caught offside.
Corner,  Málaga. Conceded by Vitolo.
Javi Ontiveros (Málaga) is shown the yellow card for a bad foul.
Luciano Vietto (Sevilla) wins a free kick in the defensive half.
Foul by Javi Ontiveros (Málaga).
Corner,  Málaga. Conceded by Steven N'Zonzi.
Attempt blocked. Ignacio Camacho (Málaga) header from the centre of the box is blocked. Assisted by Sandro Ramírez with a cross.
Corner,  Málaga. Conceded by Diego González.
Attempt missed. Javi Ontiveros (Málaga) right footed shot from the right side of the six yard box misses to the left. Assisted by Roberto Rosales with a headed pass.
Offside, Málaga. Ignacio Camacho tries a through ball, but Sandro Ramírez is caught offside.
Attempt saved. Javi Ontiveros (Málaga) right footed shot from long range on the right is saved in the centre of the goal. Assisted by Roberto Rosales.
Substitution, Sevilla. Diego González replaces Wissam Ben Yedder.
Vitolo (Sevilla) wins a free kick in the defensive half.
Foul by Gonzalo Castro (Málaga).
Substitution, Málaga. Gonzalo Castro replaces Juankar because of an injury.
Sevilla scored four goals in the space of 11 minutes as they beat Malaga and moved up to second in La Liga.