Taking the attacking reins from the injured Gabriel Jesus, Nketiah gave Arsenal lift-off in a slow-paced first half and completed his treble before Fabio Vieira's late penalty and Takehiro Tomiyasu's first Gunners goal, leaving Paul Heckingbottom's besieged troops still winless since their return to the top flight.
Electing to shuffle the pack after Tuesday's successful Champions League exertions, Arteta brought Emile Smith Rowe into the XI for his first Premier League start in 17 months, while Nketiah, Jakub Kiwior and Kai Havertz were also offered opportunities to impress.
The early pattern of play surprised no-one, as Arsenal dominated the ball and probed in and around the Sheffield United area, but Heckingbottom's depleted side held their shape and defended well.
A few exquisite passes from the under-fire David Raya - preferred to Aaron Ramsdale once again - were the highlights of an otherwise forgettable opening 20 minutes, but with their first shot on target, Arsenal belatedly made the breakthrough in the 28th minute.
Club-record signing Declan Rice was the instigator, picking up the ball in the right-half space and fizzing a pass into Nketiah, who produced a deft touch to evade ex-Arsenal man Auston Trusty before an emphatic finish low into the net.
As was the case after the 2022 World Cup, Nketiah stepped up in the absence of a stricken Jesus, whose compatriot Gabriel Martinelli nearly made it two for Arsenal in the 41st minute, but Wes Foderingham did well to keep out his venomous drive.
While Arsenal only held a narrow lead at half time, it was a merited one, as the Blades offered little to no attacking threat whatsoever, and their uphill climb would become all the more difficult with five minutes gone in the second half.
An inswinging corner from Bukayo Saka headed for the gloves of Foderingham inside the six-yard box, but the Blades goalkeeper spilled the ball, and Nketiah arrived on the scene to find the top corner with a pinpoint half-volley.
Sheffield United were up in arms, as they felt that Ben White had illegally impeded Foderingham, but the goal was awarded following a VAR review, and Saka's assist saw the Englishman register a direct goal contribution for the seventh Premier League game running.
No English player achieved that feat for Arsenal since Ian Wright in 1994, but Saka's compatriot Nketiah was hogging the spotlight and completed his first Premier League hat-trick in some style with 58 minutes on the clock.
Combining with fellow Three Lions man Smith Rowe, Nketiah received the ball on the half-turn from his colleague and unleashed an unstoppable 25-yard strike into the top corner, thereby registering his second Arsenal treble after scoring his inaugural Gunners hat-trick against Sunderland in the EFL Cup in December 2021.
Before taking home the match ball, Nketiah would also take the captain's armband off Saka as Arteta made an expected raft of late substitutions, one of whom - Vieira - won a penalty in the dying embers after being scythed down by Oliver Norwood.
Arsenal made to wait for a lengthy VAR check to confirm the spot kick, but Nketiah would unselfishly pass on the opportunity to join Thierry Henry and Andrey Arshavin in the Gunners' Premier League four-goal club, as Vieira stepped up and sent Foderingham the wrong way in the 88th minute.
Ten minutes of added time was the last thing that Sheffield United wanted to see, and their humiliation worsened in the sixth, as Vieira's corner was flicked into a packed six-yard box by Mohamed Elneny, and Tomiyasu swivelled and poked home his first goal for the Gunners on his 50th Premier League appearance.
Moving onto 24 points from their opening 10 games, Arsenal have temporarily jumped above Manchester City into second place - two points behind Tottenham Hotspur - while Sheffield United remain dead last and are now the only side in the Premier League without a win owing to Bournemouth's beating of Burnley.
The Gunners now have an EFL Cup third-round London derby with West Ham United on the agenda for Wednesday, while Sheffield United aim to make it 11th time lucky at home to Wolverhampton Wanderers on November 4.