A win would have seen Jorge Sampaoli's men move three points clear of Barcelona following the reigning champions' 1-1 draw with Real Betis earlier on Sunday, while also leapfrogging Real Madrid ahead of their clash with Real Sociedad later on Sunday.
But Sevilla found themselves in deep trouble after just two minutes when Nico Pareja was shown a straight red card for bringing down Pablo Piatti inside the area, with Jose Reyes keeping his cool from 12 yards against his former team.
Sevilla refused to throw in the towel, though, and Stevan Jovetic restored parity in the 20th minute with a right-footed shot from close range after being set up by Samir Nasri.
Espanyol went a goal up once more late in the first half, Marc Navarro heading home after Reyes' free-kick and Gerard Moreno then put the match to bed with just under 20 minutes left when he beat goalkeeper Sergio Rico with a header from the centre of the box.
Sevilla sit third in the table following Sunday's results, level on points with second-placed Barcelona and one point behind Madrid, who have two games in hand.