Joan Capdevila's own goal gave the home side an early lead with Andujar Coke and Alvaro Negredo scoring the second and third in the space of four minutes as Sevilla looked comfortable throughout their 3-0 win.
The result means Los Rojiblancos are now three points adrift of seventh-placed Real Betis, who occupy the last European berth, with four games remaining ahead of their match with Barcelona.
Espanyol remain in 11th place with nothing more than pride to play for in their remaining fixtures against Real Madrid and struggling Deportivo La Coruna.
Sevilla dominated the game against Sunday night's visitors, who had started the day side by side with them on 43 points.
Espanyol tried their luck with a couple of wayward chances early on before Capdevila handed the initiative to the home side with his 11th minute own-goal.
Sevilla midfielder Jesus Navas fired in a cross and Capdevila tried to make a block, but he ended up heading the ball into his own net from 12 yards out.
Coke then doubled the home side's lead after he linked up with Navas on the right, before Negredo made the result safe in the 22nd minute when he slotted home Ivan Rakitic's assist.
Sevilla continued to pressurise Espanyol after the break, with Negredo's 20-yard effort testing goalkeeper Francisco Casilla before Capdevila almost atoned for his error at the other end when Antonio Beto was forced to save his 73rd-minute strike from the edge of the box.
However, Espanyol were unable to find a breakthrough as their evening ended in frustration, while for Sevilla, the prospect of European football remains just about alive.