Two early goals left many predicting a white wash but a header from Tim Cahill reinvigorated his side and they came close to snatching a point before Jean Beausejour's late hitChile in their World Cup Group B opener against Australia.
Jorge Sampaoli's men stormed out of the blocks in the Group B affair, with Alexis and Valdivia on target inside 14 minutes.
Australia's all-time leading scorer Tim Cahill popped up to head a goal back for Ange Postecoglou's side on 35 minutes, as they steadied the ship.
And despite several chances - multiple off the head of Cahill and a brilliantly-taken volley from midfielder Mark Bresciano - Australia could not find an equaliser, and Chile sealed the three points when second-half substitute Beausejour struck from outside the area in injury time.
The South American nation dominated from the outset, and while they attacked down the left channel in the opening 10 minutes, they would soon garner much more joy from the other side of the Arena Pantenal.
Australia's time on the ball was minimal, although their one path to get in behind the Chileans would have been to draw their wingers forward and release the likes of Tommy Oar and Mathew Leckie.
Chile turned their possession dominance into a two-goal lead inside 14 minutes, with star forward Alexis and Valdivia finding the back of the net.
Alexis finished after some scrappy Australia defence allowed Charles Aranguiz onto the right byline, and his chipped cross found the head of Eduardo Vargas.
Vargas did not connect firmly with his header, and it fell fortunately to Alexis, who side-footed into the back of the net, despite Australian custodian Mat Ryan getting a hand on the effort.
Moments later, Valdivia was left unmarked at the edge of the area, and Alexis found him with a pin-point pass and the Palmeiras midfielder tucked his shot in off the crossbar to double the South American nation's advantage.
Australia found their footing in the contest, when Cahill buried a vintage header in the 35th minute.
Ivan Franjic's cross from the right found the New York Red Bulls striker in the box, and he leapt higher than Chile centre-back Gary Medel to power home past Bravo.
Cahill almost made it two in as many minutes, but Bravo was up to the task with his right-foot effort from a tight angle as Australia's belief grew.
Their new-found confidence also saw them susceptible at the back when Mauricio Isla got in behind, forcing Australian left-back Jason Davidson to clear for a corner.
Injury struck the Australians early in the second half - with Ryan McGowan replacing right-back Franjic - although it did not halt their push for an equaliser.
Oar found the head of Cahill with a brilliant ball from the left on 50 minutes, although he failed to connect with any vigour - and the front man claimed he was fouled in the area.
And Cahill was left more frustrated as his buried header in the 53rd minute was disallowed, albeit rightly so, by the offside flag.
Bresciano then fired a left-foot volley on target, forcing Bravo to save low to his left as Australia's pressure from crosses intensified.
Bravo finally decided to clear the danger himself on Australia's next ball into the box, storming off his line to collect in a small win for Postecoglou's men.
However, Chile were always just one goal away from seeing off the Australian resurgence, and Vargas poked a goal-bound effort past Ryan only for centre-back Alex Wilkinson to clear off the line.
Leckie was running hard at Chile's defence, and his barnstorming run in the 66th minute failed to see him fire off a shot, but the FSV Frankfurt man had put left-back Eugenio Mena on notice.
Cahill kept jumping, and in the 70th minute sent a header just over Bravo's crossbar.
But there would be no late joy for the Australians, as Chile held on to gain a vital three points for their knockout-stage hopes as Beausejour drilled a fine effort across goal and into the bottom-right corner in injury time.