Sevilla needed to win and hope three other results went their way, but despite Alvaro Negredo's opener in first-half injury time they were pegged back by a 77th-minute strike from Philippe Coutinho.
Jesus Navas had the first chance for the visitors in the seventh minute when he brought a save out of Espanyol goalkeeper Cristian Alvarez, while at the other end Andres Palop saved a Joan Verdu free-kick.
Ivan Rakitic and Diego Perotti both had chances for Sevilla and Juan Cala missed a fine opportunity when he headed over from a Jose Reyes free-kick, before Negredo broke the deadlock just before the interval by heading home a Rakitic cross.
Perotta came close to increasing Sevilla's lead when he headed wide at the start of the second half, then Espanyol keeper Alvarez was forced to make a superb save to deny Barrera Deivid from 25 yards.
Espanyol went on to force a succession of corners and their pressure finally told in the 77th minute when Joan Verdu sent the ball into the area for Coutinho to fire a rising shot into the top corner from 12 yards.
Frederic Kanoute almost snatched the lead back for Seville in the 86th minute when he headed a Rakitic cross just over, and moments later another Rakitic cross was bundled to safety by Juan Forlin.