After being dismissed for 295 early on day two, the home side battled back in the 78 minutes' batting time to lunch when Ryan Harris coaxed an edge off Cook to wicketkeeper Brad Haddin for 13.
It was a psychological breakthrough for the Australians after Cook scored an unbeaten 235 in the drawn corresponding Test at the Gabba ground three years ago.
Recalled pace bowler Mitchell Johnson followed up snaring the wicket of Trott, who tickled one down the leg-side to Haddin for 10 leaving the tourists on 55 for two at lunch.
Trott proved a big success in the last Ashes series in Australia, scoring 445 runs at 89.00 with two centuries.
The first innings by Australia, defending a 25-year unbeaten record at the famous Brisbane ground, ended on 295 when Haddin was run out chasing a century.
The veteran wicketkeeper, 78 not out overnight, attempted a risky second run on 94 but was beaten by Carberry's throw from deep point to Matt Prior behind the stumps.
Haddin faced 153 balls and hit eight fours and a six in his spirited knock which steadied the Australian innings after teetering at 132 for six.
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