After a run of three straight draws, Julen Lopetegui's side was looking to take all three points against Elche, fresh off a 3-1 win against Alaves last time out, and thanks to two goals in five second-half minutes, the hosts did just that.
Papu Gomez was the first to strike in the 70th minute, finishing off a blazing run down the left wing by cutting inside and firing a shot past Edgar Badia in the Elche goal.
Five minutes later, on-loan star Anthony Martial sent in a cross from the same flank, which Rafa Mir nodded into the net to kill off any hope Elche had of victory.
The win, Sevilla's 14th of the season, puts it on 50 points, three adrift of leader Real Madrid, which plays Villarreal on Sunday (AEDT).
But Carlo Ancelotti is likely to be without his talisman Karim Benzema, who may be be held back for the key UEFA Champions League round of 16 clash against Paris Saint-Germain on Wednesday (AEDT).
With Villarreal also fighting to stay inside the top six, the pressure is on Los Blancos to re-establish its six-point lead over second-placed Sevilla, which next faces Espanyol in LaLiga a week on Monday (AEDT).