Sanchez broke the deadlock midway through the first half and then put the home side ahead again in the opening stages of the second after Oscar De Marcos had levelled proceedings just before the interval.
Sergio Garcia then gave Espanyol a two-goal cushion in the 66th minute and while Ibai Gomez narrowed the deficit in injury time, his strike proved too little too late as Javier Aguirre's men recorded their third win of the season to move above Bilbao in the fledgling table after five games.
The visitors came into this match looking for their third successive victory at a ground where they had not come away with all three points since 1998.
They managed to subdue the Estadi Cornella-El Prat crowd in a rather dull opening, but their hard work was undone as Sanchez brought the game to life in the 24th minute with a stunning goal.
Bilbao goalkeeper Gorka Iraizoz punched away former Portugal international Simao Sabrosa's corner to Sanchez, who superbly volleyed into the top left corner from 25 yards.
Simao then headed wide from Juan Fuentes' right-wing free-kick as Espanyol started to take a stranglehold of the game.
Yet they were punished two minutes before the break as Bilbao equalised with their first real sight at goal after Aritz Aduriz's cross from the right side of the penalty box was slotted home by De Marcos.
The goal failed to change the momentum as Espanyol came storming out of the blocks and regained the lead four minutes after the resumption.
Garcia's right-wing cross was turned in by Sanchez for his and the Periquitos' second goal of the evening.
De Marcos narrowly struck over with his effort from just outside the area before Garcia established a two-goal lead in the 66th minute.
It was a touch unfortunate for Iraizoz, who made superb saves from Christian Stuani and Garcia but was powerless to stop the latter from following up his own rebound.
It left Bilbao with a mountain to climb in their bid to end a 15-year winless run against their opponents although they refused to surrender.
Aduriz headed over the bar and Gomez missed the target from distance, while they were still vulnerable at the other end as Gabriel Torje saw a shot from outside the area saved by Iraizoz.
Gomez did set up a tense finale when he fantastically netted with a superb strike from 35 yards, but it proved scant consolation for Bilbao, who could not fashion any more chances as Espanyol held on.