The Colombian struck in stoppage time after Jakub Kiwior’s own goal had given the Reds the lead at Emirates Stadium.
Jürgen Klopp’s men will discover their opponents in the next stage of the competition on Monday night.
Here are five things we noticed in north London…
A celebration for the ages
There were 10 minutes remaining when substitute Ryan Gravenberch won a free-kick deep in the Arsenal half, and right in front of the travelling Liverpool supporters.
From the left flank, Trent Alexander-Arnold delivered it into the danger area, and as both Diaz and Diogo Jota went after it, the ball deflected off the head of Kiwior and beyond Aaron Ramsdale. Suddenly, a tight game was open.
The celebrations which followed told their own story, Liverpool’s players enjoying the moment in front of a delirious away end. Diaz would go on to give them even more to shout about.
Diaz back in the goals
An assist at Burnley, a fine display against Newcastle United and now a first goal in eight games; Diaz has had a pretty good festive period.
The No.7 was a difference-maker here, moving to the right flank in the second half after a tough opening 45 on the left, and causing Arsenal all kinds of problems in the process.
Only a fine save from Ramsdale denied Diaz the opening goal, 18 minutes from the end, but after Kiwior’s own goal, the forward was there to see off the Gunners in the closing stages, hammering home from Jota’s pass to cap another encouraging display.
He now has six goals for the season, equalling his best tally in a campaign for the club.
Konate stands tall again
Player of the Match in the Premier League meeting between these sides at Anfield last month, Ibrahima Konate was equally impressive here.
Starting alongside Jarell Quansah at the heart of the defence, the France international stood tall against Kai Havertz and co, making a huge block early on to deny Reiss Nelson and standing firm in the second half as the home side chased the win through Bukayo Saka and Gabriel Martinelli.
The Reds had to soak up some pressure here, but with Konate at his very best, this was a victory built on solid foundations.
Jones shows his growth
Five years ago this very day, Curtis Jones made his senior Liverpool debut in an FA Cup third-round defeat at Wolverhampton Wanderers.
Here, we saw just how far the 22-year-old has come since that day.
This was the midfielder’s 117th game for the Reds, and one in which he showed all of the confidence, energy and quality we know he possesses.
His pressing, as ever, stood out, and even when he moved to a deep-lying role in the second half, he was able to influence proceedings.
The boy is now a man.
Subs make their presence felt
A theme of this season, so far, has been Klopp’s ability to look to his substitutes’ bench and find solutions to problems, and that was evident again here.
All four of Liverpool’s replacements made an impact. From Gravenberch winning the free-kick which led to the opening goal, to Jota’s assist for Diaz and the mature displays of youngsters Conor Bradley and Bobby Clark in the closing stages, the Reds had everything covered.
No wonder the boss was smiling at the end.
