The feat achieved by Berekum Chelsea is the best ever attained by an African side in a competition which dates back to 70 years.
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Jonas Attuquaye registered the match opener in the 16th minute, before Jhefer David restored parity for Paranaense eight minutes after the first half break.
The game produced no more goals and the centre referee was compelled to usher the two clubs into penalty shootout to break the tie.
The Ghanaian outfit reigned supreme in the shootout as they defeated their more fancied side Atletico Paranaense 8-7 to progress to the quarters and made history as the first African club to do so.
Several footballers have benefitted from their participation in the Viareggio Cup, including former Ghana skipper Stephen Appiah with Udinese of Italy.
Berekum Chelsea will take on the U-19 side of Italian outfit Genoa on Friday 22nd March in their bid for a place in the last four of the competition.