Chile got the victory they needed if they are to have any chance of progressing from a daunting Group B when they held off a strong Australian fightback to emerge 3-1 winners in another open and entertaining World Cup clash on Friday.
Alexis Sanchez put Chile ahead from close range after 12 minutes and two minutes later Jorge Valdivia made it 2-0 with a well-struck shot as the South Americans looked in control.
Australia fought back strongly, though, and Tim Cahill replied with a header after 35 minutes and thought he had equalised with another early in the second half only to have it ruled offside by an excellent linesman's decision.
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.
Within two minutes Chile were two up, carving their way through Australia's defence before Sanchez squared for Valdivia to rifle into the roof of the net from the edge of the box.
A heavy defeat looked on the cards for the Socceroos but Chile sat back and allowed them to settle.
Australia's record goalscorer Cahill got above Gary Medel to head powerfully home and the striker was denied again moments later when his low strike was saved by Claudio Bravo.
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.
Australia had a let off when Alex Wilkinson got back to clear off the goalline from Eduardo Vargas but Chile could not relax.
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.
Image: Alexis Sanchez of Chile shoots and scores his team’s first goal past Australia’s Matthew Spiranovic and goalkeeper Mathew Ryan.
Photograph: Stu Forster/Getty Images