Brendan Rodgers' side hammered Arsenal 5-1 at Anfield in the Premier League last weekend, but the north London club restored some pride by avenging that defeat to set up a last-eight encounter with Everton.
Alex Oxlade-Chamberlain handed the hosts 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.
The England international then turned provider shortly after the interval, pulling a ball back for Lukas Podolski after a smart one-two between himself and Mesut Ozil.
|VIEW FROM THE EMIRATES
|By Greg Stobart
The guttural roar from the raucous home supporters at the final whistle reflected the importance of this win to a club that have not won a trophy since 2005.
Arsenal needed a little luck and plenty of character to hang on in the final stages - but this was a huge win for Arsene Wenger’s side as they battle on three fronts, with a Champions League clash against Bayern Munich next up here on Wednesday.
Alex Oxlade-Chamberlain and Lukas Podolski scored the goals for the visitors, while at the other end deputy goalkeeper Lukasz Fabianski was in inspired form to deny Liverpool’s strikers.
The visitors did score from the penalty spot and were only denied another spot-kick by a dire refereeing decision from Howard Webb after Luis Suarez was hacked down by Oxlade-Chamberlain.
Webb should also have sent-off Steven Gerrard for a second booking, much to the fury of the home supporters. But they go home happy and in a great position to end their trophy drought in the final three months of the season.
Daniel Agger almost grabbed a dramatic equaliser with four minutes left when he headed wide after Lukasz Fabianski flapped at a delivery from Gerrard, but Arsenal stood strong to reach the quarter-finals for the first time in three years.
The Gunners, with one eye on Wednesday's Champions League clash with Bayern Munich, made seven changes from Wednesday's goalless draw with Manchester United, while Liverpool's only notable switch came in goal as Brad Jones replaced Simon Mignolet.
Daniel Sturridge had two early chances for Liverpool, forcing Fabianski into an early save after just a minute before latching onto Suarez's clipped through-ball, 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.
Liverpool recovered well and enjoyed a strong spell of possession, but struggled to force Fabianski into any further saves.
A more accurate cross from Podolski seven minutes before the break would have offered Sanogo a chance to double Arsenal's lead, while Suarez got a shot away on goal two minutes before the break, only for Fabianski to palm away with a strong right hand.
Podolski did, however, extend the home side's advantage 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, before Agger then came close to hauling the sides level late on but headed wide with the goal gaping.
Having this week been described as a "specialist in failure" by Chelsea manager Jose Mourinho, who saw his side dumped out of the competition by Manchester City on Saturday, Wenger will now be especially keen to go all the way in the FA Cup.