A rocket from Geoffrey Kondogbia put Valencia on their way to victory midway through the second half soon after Marcelino received his marching orders and Santi Mina sealed the victory late in the game.
"The big teams also win like this. The important thing was to win".
Marcelino surprisingly left top scorer Simone Zaza and on-loan Paris Saint-Germain forward Goncalo Guedes on the bench and that decision almost backfired as Valencia struggled to gain a foothold in the first hour.
Espanyol had the better of the opening exchanges in the first half and could of perhaps open the scoring had Sergi Darder's shot not clipped the woodwork.
Gerard Moreno struck the post while Sergio Garcia and former Valencia man Pablo Piatti narrowly missed the target.
The pressure Valencia were under was seen on the sidelines as Marcelino was sent to the stands for his protests towards the officials and is now likely to be banned from the touchline against Barca. With 11 games gone they are still unbeaten, having won eight times and drawn three games.
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Espanyol's misery was complete in the 82nd minute when an attempted chest back to 'keeper Pau Lopez from Victor Sanchez went horribly wrong and Santi Mina nipped in.
At the other end of the table, Malaga came from behind to edge a five-goal thriller against Deportivo la Coruna 3-2 to move off the bottom of the table. Uruguayan midfielder Gonzalo Castro and striker Borja Bastón scored the crucial goals for Malaga.
Las Palmas fans waved white handkerchiefs and jeered their team after they dropped to last place with a 2-0 defeat to Levante.
Cheik Doukoure gave Levante a 72nd-minute lead before Jason added a second goal with a fine solo effort.
Athletic Bilbao snapped their three-game losing streak thanks to a characteristic towering header from Aritz Aduriz 13 minutes from time in a 1-1 draw at home to Villarreal.
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