The 26-year-old struck with his first touch after replacing the injured Ben White to set the Gunners on course for a 2-0 win as Eddie Nketiah wrapped up the fourth-round victory with a tap-in.
Arsenal have now reached at least the quarter-finals of the Carabao Cup in five of the last six seasons.
Arsene Wenger’s side lost the 2018 final to a Manchester City team that had Arteta on the coaching staff – a 3-0 defeat in which Chambers started as part of a three-man defence.
Now the thrice-capped England international is keen to go one better, having rarely featured in the Premier League recently.
“We want to go all the way,” he told Arsenal Media. “A club like Arsenal needs to be going all the way and competing for silverware in every competition, so that’s obviously our aim.
“That’s our goal, we’re fully focused on that and believe we can do that.”
The goal for Chambers was his first in over two years and he ran straight over to the bench he had stepped from just 21 seconds earlier to celebrate with his teammates and coaching staff.
“They were all getting in my ear as I came on, saying, ‘you’re going to score on your first touch,’ and it convinced me so I had to go and run over to them and celebrate,” he added.
“It happened pretty quick. All the guys on the bench who were putting me on, the set-piece coach Nico [Jover], the boss, they all said: ‘Go and score on your first touch.’
“So that was all that was in my head and, yeah, it was nice to see it come off my head and go over the line. It was definitely a first and a pretty unique way to score.”
While Leeds will now go back to focusing on addressing their recent poor league form, there were some positives for Marcelo Bielsa.
England midfielder Kalvin Phillips came through the game unscathed on his return to the side following a calf injury, while teenage defender Cody Drameh made his debut.
“It is bittersweet,” the 19-year-old told LUTV. “I am happy to make my first-team debut, but we didn’t get the result and we got knocked out of the cup.
“So it is disappointing, but I am happy to have made my debut. I have got to keep working hard in training, keep pushing myself and showing the manager I am ready.”
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in