Arsene Wenger's men got revenge for their drubbing at Anfield thanks to goals from Lukas Podolski and Oxlade-Chamberlain, and will now host Everton in the sixth round.
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 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.
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.
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 equalizer with four minutes left when he headed wide after Lukasz Fabianski flapped at a delivery from Gerrard, but Arsenal stood strong to reach the quarterfinals 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 end line.
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. Sturridge then almost drew Liverpool level, only for Fabianski to deny him when he looked to have rounded him.
Liverpool felt it 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 bringing the sides level late but headed wide with the goal gaping.