The hosts started brightly and took the lead when Raul Baena headed in from Thievy Bifouma's flick-on after 26 minutes.
Espanyol doubled their advantage just before half-time as Allan Nyom was harshly penalised for a trip on Vladimir Weiss and Joan Verdu slotted home the penalty.
Rui Fonte wrapped up the points in the second half.
Radamel Falcao scored a hat-trick as Atletico Madrid claimed their first away win of the league season in stunning style with a 4-0 demolition of Real Sociedad.
Club record signing Falcao opened the scoring from the penalty spot in the third minute and, after Adrian Lopez had doubled Atletico's lead just after half-time, the Colombia international completed his treble with two more goals late on.
Sevilla survived the second-half dismissal of defender Federico Fazio to claim a 1-1 draw against derby rivals Real Betis at the Estadio Manuel Ruiz de Lopera.
Exteberria Benat's free-kick put Betis in front but Alvaro Negredo equalised before half-time.
Fazio was given his marching orders with just over 20 minutes remaining but the 10 men managed to keep their opponents at bay in the closing stages.
Miku scored the winner seven minutes from time as Getafe came from behind to claim a 2-1 win and end Racing Santander's five-game unbeaten run since Juanjo Gonzalez took charge.
The hosts were gifted a 13th-minute lead as Adrian intercepted Rafa Lopez's wayward pass across his own penalty area and squared for Christian Stuani to roll into an empty net.
However, the visitors were behind for only 12 minutes as Jaime Gavilan showed great technique to control and guide home a volley with the outside of his foot from just inside the area.