Benzema, left unattended in the middle of the box, converted a perfect cross from Jeremy Menez in the 55th minute to settle a match played at the scene of France's 3-0 triumph over the same opponents in the World Cup final 13 years ago.
Brazil started well but the game turned when Hernanes was sent off in the 40th minute for kicking Benzema.
After the interval, France, who are regaining their form after last year's first-round exit and off-field controversies at the World Cup in South Africa, put on a more spirited display.
"Obviously, playing with 11 men against 10 made things easier but I liked what I saw", France coach Laurent Blanc said. "I think Karim had a great match."
France confirmed their upwards progress and grabbed their fifth success in a row after two initial defeats under Laurent Blanc's orders while the Brazilians slumped to their second defeat in a row after a 1-0 loss to Argentina in the Autumn.
Blanc also found satisfaction in his central defensive pair composed of Lille's Adil Rami and AS Rome's Philippe Mexes who produced a solid display.
Brazil had the upper hand in the first half, Mano Menezes's men creating chances through Alexandre Pato and captain Robinho following poor clearances by goalkeeper Hugo Lloris.
The breakthrough came 10 minutes after the interval when Benzema once again rewarded the faith shown in him by Laurent Blanc, despite average performances for Real Madrid, with the game's only goal.
Benzema has now scored in France's last three matches and will hope Real coach Jose Mourinho had an eye on his performance to snatch more time off the bench at the Bernabeu.
"Unfortunately the referee was very strict with Hernanes and the red card had a big impact on our team", new Chelsea recruit, defender David Luiz said. "But we had a good spirit, we fought until the end and some lessons will be important for us in the future."
"We mustn't get over-excited. The important game will be against Luxembourg. After our success in England, now Brazil, we are on a good run," goalkeeper Hugo Lloris said.
"This victory is the icing on the cake," midfielder Florent Malouda added. "We have to savour it."
