Following a keenly contested opening stanza, the home side really stepped up after the break.
Mikel Arteta then brought on Chambers and the substitute broke the deadlock barely 10 seconds after coming on, heading home from a corner that Leeds failed to clear.
With the advantage finally in the bag, the Gunners had the momentum in their favor. Soon enough, they doubled their advantage when former Leeds man Nketiah bundled into an empty net on the break.
Leeds huffed and puffed for consolation late on but to no avail.
Arsenal now learn their fate for the next round on Sunday when the draw for the last-8 is made.
Here are the player ratings for Arsenal:
Bernd Leno - 7/10
Leeds really gave him a tough night, calling him into action on various occasions and forcing him into five saves. Nonetheless, he went home with a clean sheet.
Cedric - 7.5/10
Absolutely unstoppable all night, although his end-product was lacking as Cedric completed just one of his nine crosses. He also went into the referee's book in the second half.
Ben White - 6.5/10
He was unsettled by Leeds' high press but didn't put a foot wrong. His night was unfortunately curtailed by an injury just 10 minutes into the second-half.
Rob Holding - 6/10
Arsenal's captain for the occasion, Holding, saw a header blocked early on but turned in an assured performance in defense, blocking one shot and making three clearances. He was substituted in the 76th minute for Nuno Tavares due to an injury.
Sead Kolasinac - 6/10
He started the match brightly, showing a lot of attacking intent which caused chaos in the Leeds half but faded as the match wore on.
Mohamed Elneny - 6.5/10
The Egyptian couldn't stop any of Leeds' counters in the first-half but looked composed in open play.
Ainsley Maitland-Niles - 7.5/10
Maitland-Niles was the more active of the two central midfielders as he often got into Leeds' way, putting in a fine defensive performance.
Nicolas Pepe - 6/10
Pepe set Nketiah on the way for Arsenal's second of the night, bagging an assist.
Emile Smith Rowe - 6.5/10
Arsenal's rising star didn't enjoy a productive evening as he'd have liked, even smashing a half-decent chance wildly over the bar in the first-half.
Gabriel Martinelli - 5.5/10
The Brazilian looked lost for most of the game and then headed an effort from a free-kick wide off target. He completed only 14 passes in over 90 minutes of action.
Eddie Nketiah - 7/10
He struggled to fully trouble Leeds but then bundled home a scrappy finish in the second-half to double Arsenal's lead.
Callum Chambers - 8/10
It took him just about 10 seconds to break the deadlock for Arsenal after coming on. What a way to introduce yourself in the game!
Alexandre Lacazette - 6/10
The Frenchman was left chasing shadows for most of the time. He came really close to scoring a third for Arsenal in the dying embers of normal time.
Nuno Tavares - N/A
The young Portuguese forward made a lot of runs but didn't have enough time to make a significant impact.
Albert Lokonga - 6/10
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He was beaten off the ball by Joe Gelhardt late on but luckily the latter's effort could only hit the side-netting.