Flu have been under a caretaker coach since 2010 title-winning coach Muricy Ramalho resigned in March and agreeing for Braga to take charge once he had left Al-Jazira of the United Arab Emirates.
Striker Willian scored both Corinthians goals, first with a header in the sixth minute from captain Danilo's cross and a penalty after half an hour following a foul by Leandro Euzebio on Liedson.
Since Ramalho's departure, Fluminense have been knocked out of the South American Libertadores Cup in the round of 16 and lost two of their four Brazilian championship matches. Ramalho has since steered Santos to the Libertadores Cup final.
"I'm upset by the goal at the beginning of the game which I had warned we must not concede," Braga told reporters.
"But I am happy with my team's attitude because it's difficult to mess around with the players' heads.
"They understood and believed. For me, it was the start of a good understanding. Not so good for the result."
Corinthians are in second place on 10 points, two behind city rivals Sao Paulo who beat Gremio 3-1 on Saturday with two goals from Brazil youth international Casemiro and are the only team with a perfect record after four matches.
Luiz Felipe Scolari's Palmeiras are third with eight points after a 2-2 draw away to Internacional to remain among a group of four unbeaten teams.
Young Brazil striker Leandro Damiao salvaged a point for the home side heading a last-minute equaliser.
Ramalho's Santos, resting key players for Wednesday's first leg of the Libertadores Cup final away to Penarol of Uruguay in Montevideo, fielded reserves in a 1-1 draw with Cruzeiro on Saturday.
Vasco da Gama, whose victory over Coritiba in last Wednesday's Copa Brasil final secured their place in next year's Libertadores Cup, drew 1-1 at home against Figueirense. (Writing by Rex Gowar in Buenos Aires; editing by Greg Stutchbury; to query or comment on this story email sportsfeedback@thomsonreuters.com)
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