The Paraguay international's 7th minute strike was enough to ensure the Primeira Liga side finished above Switzerland's Basel to progress to the knockout stages
The Paraguayan struck early to condemn Otelul to a winless campaign, and his side can now look forward to a favourable draw after topping the group.
The match began with the hosts dominating possession, and it was no surprise when they took the lead with just seven minutes on the clock.
A neat ball from Axel Witsel found Nicolas Gaitan on the right side of the area; the Argentina international produced some neat footwork before sliding the ball across goal, to leave Cardozo with a simple finish.
The game lacked pace after the early goal, with chances at a premium. However, the visitors missed a good opportunity to level the tie when Laurentiu Iorga found himself in space on the edge of the box, but the Romanian’s tame effort was easily stopped by Artur.
The hosts were still controlling the play and, just over half an hour in, Cardozo almost doubled his tally seeing his powerful drive fly just past the post.
Later in the half Galati began to impose themselves on the game, and on the stroke of half-time they almost found the equaliser. Liviu Antal picked up the ball on the right flank before cutting past Emerson, and forcing Artur into a good save with a low drive.
The second half began at a pulsating pace, with Branko Grahovac pulling off a great save to deny Bruno Cesar’s powerful volley just three minutes after the restart.
The game suffered another lull with a struggle for clear chances until the 60th minute, when Javi Garcia almost doubled Benfica’s lead with blistering strike from the edge of the area.
Unfortunately for the former Real Madrid youth prospect, he saw his effort go just inches past the post.
With just over 15 minutes to go, substitute Nolito missed a glorious opportunity to kill the game off; a neat one-two with Cardozo put the former Barcelona forward through on goal, but his first-time effort flew straight at Grahovac.
The result ensured that Benfica topped Group C unbeaten to progress to the knockout stages, while Otelul Galati exit the competition bottom of the group, with no points from their six matches played.
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