Brendan Rodgers' side hammered Arsenal 5-1 at Anfield in the Premier League last weekend, but the London club restored some pride by holding off a late Liverpool fightback to set up a last-eight encounter with Everton.
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Alex Oxlade-Chamberlain handed Arsenal an early advantage after 16 minutes, sliding the ball home from inside the area to register a third goal from his last three appearances at the Emirates Stadium.
Oxlade-Chamberlain then turned provider shortly after the interval, pulling a ball back for Lukas Podolski after a smart one-two between himself and Mesut Ozil.
Steven Gerrard's penalty gave Liverpool hope a minute before the hour and the visitors were aggrieved when referee Howard Webb failed to award another spot-kick after Oxlade-Chamberlain appeared to foul Luis Suarez in the area.
Daniel Agger almost grabbed a dramatic equaliser with four minutes left when he headed wide after Lukasz Fabianski came and failed to collect delivery from Gerrard, but Arsenal stood strong to reach the quarter-finals for the first time in three years.
Liverpool, meanwhile, are left to focus fully on the Premier League.
Daniel Sturridge had two early chances for Liverpool, forcing Fabianski into an early save after just a minute before latching onto Suarez's clipped throughball, rounding the goalkeeper and firing into the side netting.
Yaya Sanogo, making a rare start in place of Olivier Giroud, was then involved in a series of Arsenal half-chances before the pressure told as Oxlade-Chamberlain fired home.
The England international was on hand to side-foot home the loose ball after Sanogo's effort was blocked by Gerrard.
Podolski doubled Arsenal's lead two minutes after the break when he applied a sweeping finish to Oxlade-Chamberlain's cutback from the byline.
Suarez hit a vicious dipping effort just over the crossbar as he sought to bring Liverpool back into the game while Ozil's save was kept out by Jones soon after.
Gerrard then handed Liverpool a fighting chance from the spot after Suarez was brought down by Podolski in the area before Sturridge almost drew Liverpool level, only for Fabianski to deny him when he looked to have rounded him.
Liverpool felt they should have had another penalty when Suarez appeared to be clattered by Oxlade-Chamberlain in the area, but Webb was unmoved.
Agger then came close to hauling the sides level late on.
The win means the Gunners will face Everton in the last eight after the Toffees saw off Swansea City 3-1 at Goodison Park.
Everton boss Roberto Martinez is bidding to become the first manager to win the competition in consecutive years with two different clubs after his success with Wigan Athletic last term.
Monaco loanee Lacina Traore marked his Everton bow by opening the scoring in the fourth minute, before Jonathan de Guzman levelled matters 11 minutes later.
Substitute Steven Naismith restored the hosts' lead following a defensive lapse from Neil Tayor in the 65th minute, and Leighton Baines made sure of the win from the penalty spot shortly after.
Swansea went close to breaking the deadlock early on as Pablo Hernandez played a wonderful throughball into the path of Alvaro Vazquez, but the striker failed to make the most of the opportunity.
And the visitors were punished moments later, when debutant Traore - a towering presence in the Swansea penalty area - cleverly flicked home from close range after some good work by Sylvain Distin.
But Swansea pulled level in the 15th minute, as De Guzman stormed into the box with a perfectly timed run to power home a header from Taylor's cross.
Everton started the second half brightly, and Ross Barkley pulled the trigger from the edge of the penalty area with an effort that stung the palms of Tremmel.
But as the half progressed, it began to look increasingly likely that the sides would need to meet again at the Liberty Stadium to determine a winner.
However, after Pienaar had sent a powerful header wide of the left-hand upright, Naismith capitalised on Taylor's misplaced back pass to slot the ball underneath Tremmel and into the back of the net.
And Everton could feel sure of their place in the quarter-finals seven minutes later as Baines converted a penalty after Naismith had been felled by Jazz Richards.
In the other tie on Sunday, League One Sheffield United continued their giant-killing run, knocking over Championship side Nottinham Forest 3-1 to progress to the quarter finals.