Only two players from each side that started the FA Cup tie started in the Carling Cup battle, but the same team went through after The Gunners pulled out a barely believable result at Anfield.
Jeremie Aliadiere tormented the Liverpool defence and gave the visitors the lead against the run of play after 27 minutes, but Robbie Fowler levelled up five minutes later with a trademark classy finish.
Baptista curled in a free kick and slotted in a second either side of Alexandre Song bundling home after a Jerzy Dudek error to send Arsenal in 4-1 ahead at half time despite a largely even contest.
Baptista had a penalty saved by Dudek but completed his hat-trick soon after but a superb Steven Gerrard volley and a Sami Hyypia header gave Liverpool some hope by making it 5-3 with ten minutes left.
Baptista added a fourth though and an Arsenal sixth six minute from time after more poor Liverpool defending to make it a mind-boggling 6-3 - and Rafa Benitez's evening was made even worse as Mark Gonzalez and Luis Garcia looked to have picked up serious injuries.
The game started badly for Liverpool who lost Mark Gonzalez after just five minutes when he was stretchered off in agony after receiving lengthy treatment following what looked an innocuous challenge.
Liverpool started the better were bossing the game with Steven Gerrard's long-ranger well saved by Manuel Almunia while Craig Bellamy only just failed to fine Fowler with his cut back.
Arsenal took the lead though in simple fashion after 27 minutes as Aliadiere was allowed to run in onto a straight long ball from the back and he poked the ball home at the second attempt after Dudek partially blocked his first attempt.
The lead only lasted five minutes as Liverpool hit back with a sublime Fowler finish, with the veteran flicking in at the near post after Luis Garcia scuffed a miss-hit shot on the rebound from Fabio Aurelio's free kick.
Arsenal regained the lead five minutes before half time when Baptista, who had won a questionable free kick, curled his effort low over the wall and in with Dudek disappointingly not moving a muscle as he watched the ball ripple the back of the net.
The Gunners hit a third on 45 minutes thanks to a Dudek howler as the Polish keeper came but completely missed a corner and the ball hit Sami Hyypia's knee, and then Song's arm before bouncing over the line.
With six minutes of stoppage time due to the Gonzalez injury, there was still time for Arsenal to amazingly make it 4-1 on the stroke of half time.
Aliadiere looked offside when he was slipped in but the flag stayed down and he had time to square for Baptista to tap in his second and Arsenal's fourth in an amazing first half.
The second half started as the first had ended and Arsenal were awarded a 58th minute penalty after Hyypia had brought down Aliadiere inside the box. Dudek though produced a superb save to deny Baptista his hat-trick.
The big Brazilian would not be denied though, and just a minute later Baptista rifled a low shot past Dudek from 20 yards to incredibly make it 5-1 and have the Anfield crowd in complete bemusement.
The Kop did get a goal to celebrate and it came in some style as Gerrard fired a screamer past Almunia when he managed to control a high volley at the edge of the box which rocketed into the net.
More misery came for Benitez though on 74 minutes as Garcia followed Gonzalez in being stretchered off as he looked to have injured his knee.
Liverpool kept going though and Almunia did brilliantly to tip Gerrard's free kick onto the bar, with the follow up headed away for a corner.
The Reds did make it 5-3 with ten minutes left when Gabriel Paletta crossed for his fellow centre half Hyypia to power in a header and give the home crowd just a glimmer of hope.
All hope was snuffed out six minutes from time though as Aliadiere got the better of Paletta yet again before handing Baptista his fourth and Arsenal's sixth in an astonishing match.
There was still time for Liverpool to have a fourth goal chalked off for offside, while Almunia denied substitute Jamie Carragher with a fine tip-off as the curtain finally came down on a spell binding encounter.
