The English forward turned in from close range to open the scoring after 17 minutes.
Rather than lie down, the Black Cats responded with a goal of their own courtesy of a delightful chip from Nathan Broadhead.
Unfortunately it was the last glimmer of hope for the League One club as Nketiah restored the two-goal advantage, and then some.
With just four minutes gone in the second-half, a terrific cross from Nuno Tavares was controlled beautifully by Nketiah, who finished impressively past Lee Burge.
The 22-year-old's third and final goal was another of high quality, this time a back-flick finding its way into the bottom left after some brilliant work from Pepe.
The night got even better for Arsenal fans when exciting teenager Charlie Patino was handed his first-team bow.
The 18-year-old playmaker had a debut to remember as he scored Arsenal's fifth goal for the night with a slick finish.
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