It was Valencia who had claimed a 2-1 win in last week's first leg, but they were undone by two late goals at the Estadi Cornella-El Prat.
The German was adjudged to have been the last man and the referee didn't hesitate in showing him a straight red card.
They threatened again midway through the first half when Christian Stuani met Duarte's cross at the front post, but he ended up directing his header inches wide.
Espanyol continued to create the better chances and Alvarez fired over the bar, before Duarte saw his shot blocked on the line as the first half finished goalless.
After the break, the hosts remained well on top, but they had to wait until the 79th minute to make the breakthrough.
Caicedo was the man who found the net, as three minutes after coming off the bench he met Salva Sevilla's free kick and headed past Rodriguez.
The Ecuadorian grabbed his second of the match 10 minutes later when he was picked out inside the box by Vasquez, before drilling a low strike into the corner to seal his side's passage into the quarter-finals.