Leeds impressed in the first half but substitute Calum Chambers put Arsenal ahead with a header from a corner in the 55th minute, netting with his first touch of the game and 23 seconds after his introduction for the injured Ben White.
After a header from captain Liam Cooper to goalkeeper Illan Meslier fell short, former Whites loanee Eddie Nketiah then doubled Arsenal's lead in the 69th minute.
Graham Smyth, the YEP's chief football writer, hands out the scores as Leeds squandered an opportunity to book a place in the quarter-finals.
1. Illan Meslier
6 - Didn't have a huge amount to do in terms of saves. Might have been caught behind his line for the first but second was not his fault. Picture by Bruce Rollinson.
2. Cody Drameh
7 - Can be pleased with his debut, the first half in particular when he tackled well and got forward. Did not look overawed. Photo by Alex Pantling/Getty Images
3. Diego Llorente
8 - A superb first half, showcasing his repertoire of passing. Dictated play for Leeds. Unable to do the same in the second half before surprisingly coming off. Photo by Alex Pantling/Getty Images.
4. Pascal Struijk
7 - Solid defensively, in the main kept it simple in possession and largely allowed Llorente to try the more adventurous stuff. Photo by Julian Finney/Getty Images.
5. Stuart Dallas
6 - Had a hard time against pace in the first half but got forward really well. Less effective after the break. Photo by Bruce Rollinson.
6. Kalvin Phillips
6 - Kept Emile Smith-Rowe quiet in the first half, passed it well. Had to do a bit more chasing and looked frustrated in the second half. Photo by Julian Finney/Getty Images.