Second half goals by Diego Colotto and Sergio Garcia gave the visitors all three points, despite having far less possession than their opponents and taking half as many shots.
Manuel Pellegrini made five changes to the Malaga side that beat Porto 2-0 on Wednesday to qualify for the quarter finals of the Champions League, with matchwinner Roque Santa Cruz replacing Javier Saviola up front, and Lucas Piazon and Seba Fernandez coming in for Joaquin and Julio Baptista, who were rested.
Espanyol made the stronger start. Joan Verdu forced an excellent save from Willy Caballero just three minutes in, and the goalkeeper came to his team's rescue again a minute later, rushing out to deny Felipe Mattioni.
At the other end, Kiko Casilla did well to keep out a shot from Santa Cruz following a corner.
The opening goal arrived just four minutes into the second half, after a clanger from Caballero. The Argentinean - who has been one of the best goalkeepers in Spain this season - came out to take a corner from Verdu but failed to hold onto the ball, dropping it at the feet of centre-back Colotto, who smashed it into the net.
Malaga continued to dominate possession but were nullified by Javier Aguirre's side. Pellegrini brought on Joaquin and Duda in place of Piazon and Fernandez in search of an equaliser but not long after the pair came on, Espanyol scored again, this time from a counter attack.
Wakaso burst down the left wing and delivered a good ball into the box, which Sergio Garcia hit first time into the roof of the net.
Saviola was introduced in one final attempt to give the hosts a lift in attack, but they only created one real chance, Santa Cruz shooting wide.
Caballero prevented Espanyol from scoring again when he denied Victor Alvarez in stoppage time but his costly error which changed the game will be remembered the most.
The result was Espanyol's first win in four matches and only their third victory away from home, but takes them up to 13th place in the league, while Malaga slip to sixth.