Carberry (153no), surprisingly preferred at the top of the order ahead of Joe Root, and Cook (154no) - in his first innings of the tour after missing the opening match with a sore back - made chanceless hundreds as an England pair batted through the day for the first time since 1998.
The reward was a triple-century stand, something achieved previously just twice in Tests by any England openers, on the way to a still unbroken 318 by stumps at Bellerive Oval.
They had to come through a testing first hour against the new ball but otherwise made the most of relatively easy pickings, in conditions thousands of miles away from what they can expect in the first Test in Brisbane.
Carberry, who left especially well throughout, was outscored initially by his captain but - after taking 140 balls over his first 50 - needed only another 59 for his second, hitting 17 fours and a six in his hundred.
Cook's 183-ball century was more evenly-paced and contained some trademark cuts and back-foot forces as well as two cover-drives on the up among his 12 boundaries.
The England captain had acknowledged on the eve of this second tour match the non-negotiable requirement to avoid losing early wickets in this Ashes campaign.
His team overcame that frailty to beat Australia 3-0 at home last summer, but Cook practised what he had preached at the first time of asking as he seeks to follow up the prolific run-making which underpinned England's 2010/11 success in Australia.
He showed just occasional signs of discomfort from his back but never appeared significantly discomfited.
Carberry was at ease too, as he staked his claim to just a second Test cap to go with his previous appearance as deputy for the rested Andrew Strauss in Chittagong three-and-a-half years ago.
After his 78 in Perth last week, the 33-year-old left-hander retained his accustomed position as opener - while Root was listed to come in here at number five.
England still have leeway for further juggling, in the second innings and again next week against an Australia Invitiational XI in Sydney, before their team and batting order for the Gabba is set in stone.
But their selection for this fixture at least confirmed they are open to the Ashes contingency of Carberry to go in first - with Root then likely to be deployed at number six rather than the uncapped Gary Ballance.
Carberry and Cook needed their wits about them in the early exchanges as the new ball moved lavishly off the seam after England had won the toss on a sunny morning.
Cook played and missed several times yet was rarely close to an edge; Carberry needed 16 balls to get off the mark, with a clip off his thigh for four off Ben Cutting.
When Moises Henriques introduced left-arm spinner Jon Holland, Carberry twice used his feet to hit over long off.
He spent seven overs stuck on 44 but did not lose his cool and completed his 50 when he chiselled his ninth four off a thick outside edge on an attempted square drive off Henriques just before afternoon drinks.
When Holland returned Carberry successfully went over the top again, for six this time - and then, with his century in safe keeping, he twice repeated the dose over long on off Glenn Maxwell's off-spin.
Between mid-morning and tea, neither batsman had a remotely anxious moment, and it was not until the second new ball was taken under cloud cover that Carberry needed some luck - dropped in the gully off Ben Cutting, on 135.
By then, of course, he had already made the most of his opportunity and raised the obvious prospect that - after 10 Test match innings together, producing just one half-century stand, the Cook-Root opening partnership may be due for a break.
Meanwhile, Australia hope Shane Watson will be fit after all for the first Test, after scans on his hamstring revealed only a low-grade muscle strain.
The pivotal all-rounder, who hurt himself in last weekend's one-day international against India in Bangalore, will have "intense treatment" in Sydney to try to regain fitness to face England in Brisbane on November 21.
Australia physiotherapist Alex Kountouris added: "It goes without saying that Shane and the medical team will be doing everything possible to get him fit and available for selection ahead of the first Test."