Arsenal roared back from 2-0 down to draw against Chelsea last week to preserve their unbeaten league record.
Arsenal broke through a resolute Blades defence as Declan Rice's pinpoint pass was collected by Nketiah, who made no mistake with a close-range finish past Wes Foderingham.
Nketiah doubled up when Foderingham failed to deal with a Bukayo Saka corner and palmed the ball into the path of the England striker, who lashed home to make it 2-0. Nketiah's hat-trick was sealed in style as he smashed home from 20 yards.
The Gunners were awarded a penalty after a lengthy VAR check for an Oliver Norwood foul on Fabio Vieira, the Portuguese midfielder taking the spot-kick himself and sending Foderingham the wrong way to make it 4-0.
Another substitute, Takehiro Tomiyasu, completed the rout in stoppage time.