Trailing 2-1 after the first leg to seven-times winners Los Che, who on Monday rewarded coach Nuno with a three-year contract extension, the second leg in Barcelona was one-way traffic.
Ecuador striker Caicedo hit the net after 79 and 89 minutes to make it six goals for the season as the hosts edged to victory at Estadi Cornella-El Prat.
Also on Tuesday night, David Barral was on target with a quick-fire second-half double and Juanfran struck a late winner as Levante recorded a 3-2 victory at home to Malaga – but it was not enough as they went out 4-3 on aggregate.
Young Portugal winger Ricardo Horta put the visitors ahead midway through the first half and Recio doubled their lead seven minutes before the break.
But Barral netted two in four minutes to level the tie on the night before Juanfran claimed their third with five minutes remaining.
Spanish striker Barral thought he had scored a hat-trick at the death, with the referee ruling out his goal for handball before showing him a red card as Malaga held on to reach the last eight.