Alejandro Dominguez put the visitors ahead after 29 minutes, before a torrential downpour and the resulting water-logged pitch killed the pace of the game in the second period.
However, with hope fading for the Portuguese side, Cardozo was in the right place at the right time to prod home from close range seven minutes from time.
Olympiacos, meanwhile, made four alterations to the side that started last weekend’s 4-1 Greek Superleague win over Platanias, with Giannis Maniatis, Jose Holebas, Dimitris Siovas and Dominguez coming in for Avraam Papadopoulos, Anastasios Papazoglou, Delvin N’Dinga and former Benfica man Javier Saviola.
With both sides looking to attack from the off at the Estadio da Luz, the venue for this season's final, Kostas Mitroglou got ahead of his man in the penalty area after 10 minutes to meet a David Fuster cross from the right, but he failed to find the target with a close-range header.
An end-to-end first half continued to throw up chances for both teams – Benfica's Lima firing straight at Roberto after being sent through one on one, although the Brazilian had already been flagged for offside.
The hosts had a shout for a penalty after 56 minutes as Guilherme Siqueira felt he was obstructed by N’Dinga, but the referee waved play on.
But it was Cardozo who would have the last word two minutes later – prodding home from just a couple of yards in the aftermath of a Rodrigo corner.
