The Primera Division side faced an uphill struggle after losing the first leg 2-0 although they gave themselves hope when Park Chu-Young netted in the 55th minute.
But it was only in the dying seconds when they levelled the tie through Roberto Lago and substitute De Lucas capped a remarkable comeback in the 109th minute before Almeria's night was compounded when Aaron Niguez was sent off three minutes from time.
Real Zaragoza and Real Mallorca both progressed courtesy of the away goals rule.
Despite goals from Jude Ighalo and Diego Mainz giving Granada a 2-1 win at home, 10-man Zaragoza sealed their spot in the next round thanks to Jose Mari's strike although they were forced to hang on for a 2-2 aggregate result after Helder Postiga was sent off.
Mallorca's goalless draw at home to Deportivo La Coruna ensured their 1-1 stalemate at the Riazor in the first leg proved crucial.