A forgettable first half saw few sights of goal for either side, but in the second 45, Nketiah struck twice after Mohamed Elneny's header to set up a fourth-round meeting at Manchester City for the Premier League leaders.
It came as little shock to see Mikel Arteta ring the changes ahead of the weekend's North London derby, but the League One hosts were very rarely stretched to the extreme in the first half.
Clearly missing the midfield influence of Granit Xhaka, Thomas Partey and Martin Odegaard, Arsenal's slow-paced attacks were easy to stifle, although Oxford did not call Matt Turner into much action either.
Referee David Coote, meanwhile, was called into action to wave away furious Arsenal appeals for a penalty in the 35th minute, when Albert Sambi Lokonga's effort struck the hand of Elliott Moore.
The Oxford man was falling to the ground as the ball deflected off his hand behind for a corner, and with no VAR available to review the decision, Coote's call stood - much to the fury of those in white.
No changes in personnel were made during the half-time interval, and some fans were still returning to their seats when Matt Taylor beat the offside trap and ran through one-on-one with Turner in the 49th minute, but his toe poke on the stretch did not trouble the American.
After Leeds United loanee Lewis Bate did well to block Bukayo Saka's goal-bound effort in the 55th minute, Oxford survived a succession of corners from the Gunners, but the pressure finally told with 63 minutes on the clock.
Gabriel Martinelli won a free kick in a dangerous area after being fouled by Djavan Anderson, and Fabio Vieira's delivery from the left was on the money for Elneny to power a header home.
While Karl Robinson's side did not appear too deflated after the deadlock was broken, the playmaking quality of Vieira came to the fore once again in the 70th minute, as the Portuguese's perfectly-weighted through ball found Nketiah, who skipped past Edward McGinty and tapped home into an empty net.
Only six minutes later, the chants of "Eddie" rang out across the away end, as the 23-year-old executed a delicate chip over McGinty to make it three for Arsenal, although he was shown to have been in an offside position when receiving the ball from Martinelli.
One slight blot on the Arsenal notebook was the withdrawal of Saka through an apparent injury, but Emile Smith Rowe replaced his England colleague in his first game back since undergoing groin surgery in September.
Prior to a trip to the Etihad for the fourth round, Arsenal meet North London rivals Tottenham in Sunday's Premier League derby, while Oxford travel to Fleetwood Town in League One on Saturday.