Juninho opened the scoring before Brazil striker Fred was sent off for Fluminense.
Andre extended the lead before Carlinhos pulled one back, but Carlos Tenorio secured the win late on in the first domestic game played at the refurbished Maracana.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.