Diogo Jota, who scored on debut in the league fixture three days ago, was given his first start in attack alongside Mohamed Salah, as Pierre-Emerick Aubameyang sat out for Arsenal.
Hesitant play from Eddie Nketiah denied the Gunners a seventh minute opener when he struggled to pull the trigger, allowing Liverpool goalkeeper Adrian to get a hand on the ball in the box.
Liverpool also missed an inviting chance later on as Marko Grujic steered a cutback to the near post from Jota on the left wide of Bernd Leno's goal.
The Reds came close to taking a halftime lead after Takumi Minamino slammed off the underside of the crossbar after Leno parried Jota's diving header back into play.
Liverpool's persistence towards the end of the first half came over in the second period, as Grujic headed a free-kick onto the roof of the net while Virgil Van Dijk had Leno to a low stretch.
Leno became very busy in the Gunners' goal a few minutes later when he was forced to go down to his right and palm Grujic's first-time strike to safety.
The German was called in again on 63 minutes as he came off his line to push Jota's close-range strike for a corner-kick, and pulled off a one-hand stretch from the resultant corner to deny Grujic.
This while manager Jurgen Klopp decided to remove a few of his first-team regulars in Van Dijk and Salah, as Joe Gomez and Divock Origi replaced the duo.
Action shifted to the other end as Adrian came up with a point-blank save to keep out Rob Holding's towering header in the latter minutes following a corner.
A penalty shoot-out was needed to settle the tie after a goalless 90 minutes, and Leno was the hero in a sudden death shoot-out to help his side advance to the quarter-finals with two saved penalties.