Liverpool paid the price for not making the most of their dominance in normal time, having out-shot their opponents 16 to six.
Divock Origi and Harry Wilson, in sudden death, both saw efforts saved and with only Mohamed Elneny failing for Arsenal it was left to Willock to secure a 5-4 victory with the decisive kick, which Adrian got a hand to but could not keep out.
Unusually for matches between these two sides – the last nine Anfield meetings in all competitions have brought 48 goals – it was the goalkeepers who took centre-stage even before the shoot-out.
Mikel Arteta’s decision to stick with first-choice Bernd Leno was prescient as the Germany international made a string of saves in the second half, while Liverpool’s second-choice Adrian kept the score goalless with an instinctive stop from a close-range Rob Holding header.
It resulted in only the second goalless draw in 21 years between the pair.
Xherdan Shaqiri, who had impressed in the previous round, was left out as two clubs have enquired about signing him before the transfer deadline.
With both sides fielding second strings it was no surprise there was a drop in quality, but there should have been enough depth in both squads to have avoided a rather ordinary first half.
It only came to life a minute before the interval when Diogo Jota had a header saved by Leno with Takumi Minamino blasting the rebound against the crossbar from five yards.
The game prior to that had seen Arsenal try to break the Reds’ high line, having enjoyed some success with it in the second half on Monday, in particular trying to utilise the pace of Nicolas Pepe by isolating him against 19-year-old right back Neco Williams.
It was a tactic of diminishing returns as they failed to register a shot on target, despite the Ivory Coast international breaking clear and passing to Willock, who opted to lay off instead of shoot and Eddie Nketiah was dispossessed by the hand of goalkeeper Adrian.
The second half saw Leno given far more to do, with Van Dijk’s low flick saved well and Marko Grujic twice denied, once from distance and again from a looping header.
In between, the Gunners goalkeeper also saved from Jota, who cleverly nutmegged Sead Kolasinac with his chest control from Curtis Jones’ cross-field pass.
Arsenal’s attacks were becoming more infrequent but when they did get a overload at the far post, Williams nicked the ball off the toes of Bukayo Saka – in the starting line-up hours after his maiden England call – and from the resulting corner Adrian made his one save of note.
But it was Willock who made it eight domestic cup matches unbeaten for Arteta since he took charge of the Gunners, having led them to last season’s FA Cup triumph.