The teams produced a 5-5 thriller at Anfield before last season’s penalty shootout, won by Liverpool, but this was a considerably less exciting match.
Both sides struggled for fluency after making numerous changes from their Premier League meeting on Monday.
But after Divock Origi and Harry Wilson saw efforts saved by Bernd Leno, Joe Willock converted the decisive penalty.
Arsenal will now host Manchester City in the last eight, with all ties to be played in the week commencing 21 December.
Leno to Arsenal’s rescue
Mohamed Elneny’s miss earlier in the shootout looked like it was going to be costly, but German goalkeeper Leno salvaged the situation for Arsenal.
Leno’s excellence was a theme of the match, particularly once Liverpool – who had made nine changes from their win on Monday – got to grips with the game towards the end of the first period.
The former Bayer Leverkusen keeper brilliantly parried new signing Diogo Jota’s header and deserved some fortune when Takumi Minamino hit the crossbar with the follow up when he ought to have scored.
While Liverpool did not exactly carve Arsenal open at will, superb stops from Leno prevented both Jota and Virgil van Dijk from finding the left corner of the net after the break.
He became the first Arsenal goalkeeper to keep a clean sheet at Anfield since Vito Mannone in September 2012.
Arsenal were organised and disciplined in defence and despite Mohamed Salah joining Minamino and Jota in an experienced frontline for Jurgen Klopp’s side, they could not find the breakthrough.
‘I really have belief in Bernd’ – what they said
Liverpool boss Jurgen Klopp, speaking to Sky Sports: “If there would have been a winner in 90 minutes it should have been us but we are not in dreamland, you have to score. I liked a lot of parts of the game, we mixed it up a lot and I saw a proper performance, a lot of things we like on the pitch when you wear this wonderful shirt. A penalty shoot out is tricky, everyone knows. That is it.”
What did the performance lack? “Goals. So many things are different when you mix it up in decisive positions especially. I really liked how the boys did it, there were a lot of good individual performances, it could have been a Premier League game but here or there we lacked the last pass. There were not a lot of chances in this game because there was a lot of work from both teams closing each other down.
On Xherdan Shaqiri’s absence from the squad: “Some were not involved. It is the time of the year when some things happen in the background and you have to react – that is what we did.”
Arsenal boss Mikel Arteta, speaking to Sky Sports: “I am really happy with the performance. I think the boys were exceptional. We corrected a few things from Monday and it was superb.
“We competed much better, the level of aggression we had, the way we pressed them really high was exceptional. Bernd Leno was really good. When we needed him we had him. You need a top individual performance to win at Anfield and that is what we had tonight.
“I really have belief in Bernd. I know him really well and what he can give us. We didn’t want Emiliano Martínez to go but it was probably the right thing for both parties to do. The gap towards Liverpool is still big. We will keep improving to try and reach their level.”
On drawing his former club Manchester City: “I was waiting and enjoying the victory and then we have to play Manchester City. It is what it is, there are a lot of tough teams left in the competition and we will prepare for it.”
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