Australia fought back strongly, though, and Tim Cahill replied with a header after 35 minutes and thought he had equalized with another early in the second half only to have it ruled offside by an excellent linesman's decision.
Both sides went close in an end-to-end second half before Jean Beausejour grabbed a third for Chile in stoppage time, and they will now have to try to get something from games against Spain or the Netherlands, who thrashed the holders 5-1 earlier in the day.
Chile appeared to be coasting to a comfortable victory when Sanchez and Valdivia scored in quick succession.
Charles Aranguiz neatly kept the ball in play on the right with defenders scrambling to block him and he chipped into the middle where Eduardo Vargas and Mile Jedinak jostled for the header, the ball falling for goalscoring talisman Sanchez to poke home.
A heavy defeat looked on the cards for the Socceroos but Chile sat back and allowed them to settle.
The lowest ranked team of the 32 in Brazil began the second half strongly with Cahill's bullet header ruled out and then veteran midfielder Mark Bresciano forcing Bravo into another sprawling save, this time one-handed low to his left.
Cahill again demonstrated his renowned aerial ability when he climbed above his marker Gonzalo Jara but this time headed over.
Any hopes of securing a point vanished when substitute Beausejour drilled a low strike into the far corner in stoppage time.