A crisp turn-and-finish in the first half set the Gunners on their way before the England striker buried a poacher's finish after the break and capped a memorable day with a stunning rocket from 25 yards. Fabio Vieira and Takehiro Tomiyasu then rounded off the scoring late on in another dismal display for the Blades.
Arsenal came into the game a little wary after losing Gabriel Jesus to an injury following his Champions League heroics at Sevilla.
Yet Nketiah showed the striker's berth is in safe hands after he livened up a quiet opening quarter of the game at Emirates Stadium, which saw the Blades sit deep with little to no presence up front.
Declan Rice's opportunistic ball into the box caught the visitors unaware and Nketiah made no mistake after spinning his marker.
Arsenal sat comfortable in possession, unable to get a rise out of United, although that mattered little when Wes Foderingham flapped at a corner to gift the Gunners their second - the ball falling for Nketiah to finish with a VAR check confirming there was no foul in the build-up.
The 24-year-old ensured the match ball would be heading home with him when he drilled in his third goal from 25 yards on 58 minutes, which then drew audible gasps from around the ground as fans watched the replay on the big screens.
It could hardly have got much better for Nketiah, yet it did as captain Bukayo Saka - standing in for the rested Martin Odegaard - handed his fellow academy graduate the armband as he departed for the final 20 minutes.
Arteta handed rests to a handful of players during the second half, including Ben White and Gabriel Martinelli, while Gabriel Magalhaes was another saved from the XI.
One of those introduced, Vieira, won and netted a penalty in the final five minutes after a VAR check. Another, Tomiyasu, bagged a poacher's finish from a late corner to put the cherry on top of the cake.
The win brings them back to within two points of leaders Tottenham ahead of a Carabao Cup trip to West Ham.