Unai Emery's side had endured a miserable week as they were beaten 1-0 at Celta Vigo last weekend and lost by the same scoreline in the first leg of their UEFA Europa League quarter-final against Porto.
But they showed no sign of being out of sorts as they saw off the Barcelona side with a ruthless display at Estadio Ramon Sanchez Pizjuan on Sunday.
Sergio Garcia's penalty two minutes into the second half gave the visitors hope, but Espanyol have now won just one of their last five.
Valladolid's goallesss draw against Valencia ensured they climb above Getafe on goal difference with six games remaining.
Malaga moved up to 11th after they swept aside Granada 4-1 at Estadio La Rosaleda.
Ignacio Camacho helped himself to a first-half brace and Nordin Amrabat added a third from the penalty spot before Juanmi sealed the points. Youssef El-Arabi pulled a goal back 12 minutes from time but it was too little, too late and Lucas Alcaraz's men are just three points above the drop zone.
