Skipper Michael Clarke left the tourists toiling in the field chasing after the ball before calling a halt with just over an hour left and setting England an improbable 561 runs to take a 1-0 lead in the five-Test series.
England will have to create Ashes history to win the Gabba Test with their previous highest winning fourth innings score at 332 for seven in Melbourne in 1928.
The world record for the highest successful run chase is the West Indies' 418 for seven against Australia in Antigua in 2003, while the highest winning chase at the Gabba is Australia's 236 for seven against the West Indies in 1951.
Carberry, England's topscorer in the first innings with 40, played back to Harris only for the ball to trickle through his legs and dislodge the bails.
England went to stumps at 24 for two with Alastair Cook on 11 and Kevin Pietersen not out three.
Pietersen almost ran out his skipper when he darted off for a quick single on his first ball faced and Cook just made his ground.
Clarke and David Warner hit centuries as Australia accumulated an imposing 401 for seven, representing an overall lead of 560 as the home side set out to protect their 25-year unbeaten run at the Gabba ground.
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