Thierry Henry's superb volley sent holders Brazil out of the World Cup as France moved into the semi-finals.
Zidane and Henry combined to create France's goal
Inspired by man-of-the-match Zinedine Zidane, France were the better side in the first half, but failed to create clear chances to trouble Dida.
That changed just before the hour when Zidane swept a free-kick to the far post where it was sumptuously volleyed past the Brazilian goalkeeper by Henry.
Fabien Barthez denied Ronaldo late on to set up a semi-final with Portugal.
Prior to that save Barthez had flapped on a couple of occasions, but it was a mark of Brazil's lacklustre play that Ronaldo's shot came in stoppage time.
Brazil had strolled their way to the quarter-finals, but Carlos Alberto Parriera's side had no answer to a France team that combined defensive discipline with some wonderful attacking play.
France's route to the last eight has involved plenty of huffing and puffing, but the knockout stages have brought out the best in Raymond Domenech's side.
Zidane was magnificent throughout, while after the interval the speed of Henry and Franck Ribery unsettled the Brazilian defence.
As early as the first minute Brazil were given a glimpse of what they were to experience for the remaining 89 minutes as Zidane glided away from a succession of Brazilian tackles as he executed a quick turn and that trademark stepover.
A Zidane flick that deceived Cafu was equally breathaking, while he held off and teased Kaka by juggling the ball.
Not to be outdone, Brazil's number 10 Ronaldinho deftly touched the ball into Ronaldo's path before the Brazilian striker was closed down by the French defence.
A Zidane free-kick set up France's best chance in the first half but Florent Malouda headed over.
A minute before the interval another piece of Zidane wizardry released Patrick Vieira, who was scythed down by Juan, who was booked.
Within a minute of the second half starting Vieira went close with a glancing header from a Zidane free-kick.
As the second half developed Henry began to come to the fore, first sprinting past Cafu, then troubling Lucio, before the Frenchman's backheel nearly released Vieira.
So often in their careers with France, Henry and Zidane have failed to quite click, but on 57 minutes they combined to devastating effect.
Zidane whipped in a free-kick to the far past that Henry spectacularly volleyed past Dida into the roof of the net.
Soon after the waspish Ribery nearly created a second goal for France when his penetrative cross was almost inadvertently turned into the Brazilian goal by defender Juan.
Ribery then almost latched on to a Henry pass, but Dida just got to the ball before the Marseille winger.
The win means France have beaten Brazil in three of their four World Cup encounters.
Brazil: Dida, Cafu (Cicinho 76), Lucio, Juan, Carlos, Juninho (Adriano 63), Silva, Ze Roberto, Kaka (Robinho 79), Ronaldinho, Ronaldo.
Subs Not Used: Cris, Emerson, Fred, Gilberto, Julio Cesar, Luisao, Mineiro, Ricardinho, Rogerio.
Booked: Cafu, Juan, Ronaldo, Lucio.
France: Barthez, Sagnol, Thuram, Gallas, Abidal, Ribery (Govou 76), Makelele, Vieira, Zidane, Malouda (Wiltord 81), Henry (Saha 85).
Subs Not Used: Boumsong, Chimbonda, Coupet, Dhorasoo, Diarra, Givet, Landreau, Silvestre, Trezeguet.
Booked: Sagnol, Saha, Thuram.
Goals: Henry 57.
Ref: Luis Medina Cantalejo (Spain).
Fifa man of the match: Zinedine Zidane
This is only the fourth World Cup in which all four semi-finalists are European teams, following 1934, 1966 and 1982. The last time this happened, 24 years ago, three of the four current semi-finalists were also among the last four: Italy, Germany and France.
France ended Brazil's all-time record streak of 11 straight World Cup match wins, dating back to 1998 when they lost the final to France 3-0. That was also the last World Cup match Brazil had failed to score in.
Thierry Henry scored his sixth World Cup goal, surpassing Platini on the competition top scorer list for France. Henry now only trails France's top scorer Just Fontaine, who netted 13 goals at the 1958 World Cup. Goalkeeper Fabien Barthez made his 15th World Cup appearance, tying Maxime Bossis as most capped French player at the World Cup.
Trivia stats source: Infostrada Sports