However, a Baptista free-kick and tap in either side of Alex Song Billong's smart finish made it 4-1 at half time.
Two more from Baptista, the first from 20 yards, sealed it after he had missed a penalty, though Steven Gerrard and Sami Hyypia notched late consolations.
It was a remarkable contest and one that few would have predicted when, against expectations, it was revealed before kick off that Rafael Benitez had opted for a weakened starting XI.
Despite the Reds' weekend FA Cup exit, only Gerrard and Jerzy Dudek survived from the team that lost 3-1 to Arsenal on Saturday, and the selection proved key to the hosts' downfall, with Lee Peltier and Gabriel Paletta in particular exposed in defence.
The hosts' cause was not helped by the fourth-minute withdrawal of winger Mark Gonzalez, who sustained a serious shin injury in an innocuous challenge on Theo Walcott.
And, despite the early threat of Craig Bellamy, the writing was on the wall from the moment Aliadiere tapped home the opener, finishing at the second attempt after showing fine skill to pull down Toure's long pass.
Liverpool were level minutes later, Fowler clipping home his 31st League Cup goal behind his legs from Luis Garcia's cross-shot, but Arsenal's youthful pace and endeavour continued to cause the Reds all sorts of problems and the game was beyond doubt before half time.
Firstly, Baptista curled home a free-kick from 25 yards for only his second Arsenal goal, and then in injury time the Londoners scored two in quick succession to stun the hosts.
Song Billong made it 3-1 from close range after benefiting from a ricochet off Sami Hyypia and then Aliadiere was controversially ruled onside before pulling back to Baptista, who slid into an empty net to cap a remarkable end to the half.
A resolute start to the second half from the hosts lasted just 10 minutes as Arsenal continued their rampant display, and the Gunners could even afford Dudek's penalty save from Baptista after Hyypia had clearly hauled down Aliadiere.
No sooner had the Anfield crowd found their voice again, that Aliadiere cut back to Baptista from the left and the Brazilian drilled into the corner from 20 yards to complete his hat-trick.
Gerrard interrupted Arsenal's goal-fest with a stunning volley from 20 yards from Paletta's knock-back, but a disastrous evening for the hosts got even worse on 70 minutes when Garcia became the second player to be stretchered off with a serious-looking injury.
Still the goals continued to roll in though, and Hyypia further reduced the deficit with a near-post header.
Liverpool's mini-revival was halted five minutes from time when Baptista tapped in another cross from the equally-impressive Aliadiere - the first time since 1914 that Liverpool had conceded six goals at Anfield.
There was still time for Hyypia to see an effort ruled out for offside and Jamie Carragher's drilled effort was kept out smartly by Manuel Almunia as an extraordinary encounter continued into the latter stages.
But, despite the choruses of "You'll Never Walk Alone" from the home fans, it was the visiting support that were cheering at the end as Arsenal sealed their first League Cup win at Anfield in stunning fashion.