
The 24-year-old, who made his full England debut this month, has not scored for the Gunners since August but found bottom club United’s defence much to his liking.
Nketiah, back in the starting line-up because of Gabriel Jesus’s injury, broke the deadlock in the 28th minute with a fine finish after a pass by Declan Rice and made it 2-0 shortly after half-time with an emphatic goal after United keeper Wes Foderingham failed to intercept Bukayo Saka’s corner.
The best was saved for last, however, with Nketiah smashing an unstoppable shot into the top corner just before the hour.
A Fabio Vieira penalty in the 88th minute and a stoppage-time goal by Takehiro Tomiyasu completed the rout.
The victory pushes Arsenal up to second place with 24 points from 10 matches, two behind Tottenham Hotspur.
It was a familiar story for Sheffield United who have managed only one point from their opening 10 matches.