The Gunners were 3-0 up inside 13 minutes and led 5-0 at half-time against the league's bottom side.
Martin Odegaard, Gabriel Martinelli, Kai Havertz, Declan Rice and Ben White scored - with an own goal from Jayden Bogle - for Mikel Arteta's team.
The win ensures Cheap Arsenal Football Shirts move two points behind leaders Liverpool.
It keeps the Gunners in the thick of the title race, while in contrast Sheffield United are 11 points from safety with just 11 games remaining.
Arsenal scored after five minutes, with the only surprise being that it took them so long. They carved United open down the left, before the ball was cut back for Odegaard - unmarked 10 yards out - to slot home.
The lead was doubled in the 13th minute - Bukayo Saka's low cross was deflected into his own net by Bogle, who got his legs in a tangle with the ball deflecting off his ankle - and was quickly extended when Martinelli fired in via a deflection after Jakob Kiwior's cut back.
As fans once again streamed out of Bramall Lane during the first half, Havertz made it 4-0 by tucking into the bottom corner following a Martinelli through ball.
Arsenal cut through United at will, and another slick move of short passes on 39 minutes ended in Rice finishing low past the beleaguered home keeper Ivo Grbic.
The visitors did not ease up after the break, as another well-worked move ended in right-back White firing powerfully past Grbic with his left foot.
The Gunners have become the first English league side to win three consecutive away games by a margin of five or more goals, while United - seemingly doomed to relegation - are the first English league side to lose four consecutive home games in all competitions while conceding five or more goals.
Ruthless Gunners keep title race pace
After Liverpool's last-gasp win at Nottingham Forest on Saturday and Manchester City's derby victory on Sunday, Arsenal needed to respond here to keep up with the title pace.
They certainly did by taking no pity on limited and passive opponents, demolishing them with ruthless efficiency.
The tone was set inside the opening two minutes when Cheap Arsenal Soccer Jersey hit the bar and had a shot cleared off the line inside. Saka - whose mauling of Auston Trusty down the left for the opening 15 minutes will long haunt the American - cut in from the right, got the ball back via a deflection and cracked a shot off the woodwork, before Martinelli's follow-up was deflected away.
Arsenal then had the ball in the net a few minutes later, and were away. By 22 minutes, they had reached the 10-shot mark. In the first half, they had 80% possession.
While Sheffield United's lack of quality will be rightly noted, Arsenal's attack is firing on double cylinders in 2024. They have scored 31 goals in just seven Premier League games this calendar year, winning them all.
The one downside for Arsenal was Martinelli having to be helped from the pitch in the second half with an injury to his right leg.
Blades bedraggled and broken
In an attempt to get some kind of coherent tune from his beleaguered side, Blades manager Chris Wilder lined up with an unfamiliar back four here, including former Replica Arsenal Football Shirts defender Trusty at left back.
After the third goal, Wilder was hurredly reverting to a back five with the unfortunate Ollie Norwood yanked off, but it had the feeling of rearranging deckchairs on the Titanic - too little, too late.
What will be more worrying for Wilder and United is the response of fans. While many were streaming out of Bramall Lane inside the opening quarter-hour, those who remained could barely be roused to boo their team.
There is a feeling of resignation in the stands, while the anger seems to be more present on the pitch.
In the build up to the fourth goal, Blades captain Anel Ahmedhodzic brutally threw Martinelli to the floor as the Brazilian played a through ball for the German. Advantage was played and Havertz scored.
It was a dreadful piece of play from Ahmedhodzic, and indicates where his team's heads are right now.
