You never quite know what you will get with Mikel Arteta's side. Once it was clear the Blades were up against the good version and the outcome was inevitable.
Three-nil was the final score, because that was as many as the Gunners settled for.
It leaves the Blades 18 points from Premier League safety with 21 still to play for, though that gap could have been widened by the next time they take to the field. Due to a clash with the Duke of Edinburgh's funeral, we do not know when that will be.
Arsenal do not like coming to Sheffield and a cold night with a little snow in the air seemed a good time to test the softness of the southerners. It was the Blades' victory over them on a cold November evening last season which really moved their campaign up through the gears. Nights like that, in the days when you could stand within two metres of someone without getting a funny look and actually wearing a mask in the bank would have you frowned upon, feel such a long time ago.
This time Arsenal were far and away better than the Blades.
In his first Bramall Lane game as interim manager, Paul Heckingbottom saw his side start with a bit of verve. The recalled Oli Burke was hungry in the press and his team passed at a good tempo. Heckingbottom revealed recently that goalkeeper Aaron Ramsdale has been working on his passing and he began well, passing short when it was on, but showing good selection to drill passes into the centre-forwards when it was not.
David McGoldrick put their first shot wide after 10 minutes, finishing off a move which started at Ramsdale's feet.
The problem was that Arsenal started well too, and man for man, they have far better players than the doomed United. The Blades quickly faded as the Gunners completely took over.
As the pressure mounted, Oliver Norwood blocked a Thomas Partey shot, then intercepted a ball in from Callum Chambers but he hit his shot against Bukayo Saka, somewhat surprisingly selected in the hole with Granit Xhaka at left-back. The latter was never tested.
With Arsenal increasingly monopolising the ball, the cracks were starting to open up. The back three became a five.
Ramsdale got lucky midway through the first half, hammering a clearance into Alexandre Lacazette only for the ball to bounce back straight into his arms.
Two minutes later a pass from Ben Osborn was cut out by the excellent Dani Ceballos, whose backheel decorated a the build-up to a move which ended with Gabriel Martinelli rippling the side netting. Ramsdale reacted well when a shot from the winger deflected off Norwood and Enda Stevens blocked a goalbound effort from Chambers.
A minute later, the damn burst. Arsenal's football was lovely and again Ceballos's heel played an important part, playing Lacazette in to sweep beyond Ramsdale. Only Saka's poor touch stopped the goalscorer playing him in a couple of minutes later.
John Egan, up for a corner, stung Bernd Leno's fingers with a volley at the end of the half but it was a rare act of defiance, their first shot since McGoldrick's opening gambit.
The half-time interval checked the Gunners' momentum and the Blades changed shape to a midfield diamond with Osborn in the hole, but neither decisively changed the balance of power. McGoldrick had a wild shot and Norwood's mishit cross had Bernd Leno scrambling across goal but it was only the keeper who ended up in the net.
Nicholas Pepe picked Lacazette out right on the edge of the area for the centre-forward to shoot over.
In the 72nd minute Arsenal took, or rather were given, a second goal. John Lundstram, whose presence in this team is infuriating fans with the midfielder having long since decided to run his contract down, gave the ball sloppily to Pepe. Ramsdale's save only presented Martinelli with a deserved tap-in.
At 1-0, Oliver McBurnie had been brought on to inject a bit more lift into the Blades' forward line but within 20 minutes he had gone off injured.
A straight pass from Partey allowed Lacazette to score a routine third before taking the last few minutes off.
They played the second half with sensible conservatism ahead of a difficult Europa League trip to Prague, and the Blades were unable to make them have to hit the heights of the first 45 minutes.
Sheffield United: Ramsdale; Ampadu, Egan, Stevens; Baldock, Lundstram, Norwood, Fleck, Osborn; McGoldrick (McBurnie 64 (Mousset 83)), Burke (Brewster 64).
Unused substitutes: Lowe, Jagielka, Foderingham, Bogle, Bryan, Ndiaye.
Arsenal: Leno; Chambers, Holding, Mari, Xhaka; Partey, Ceballos; Pepe, Saka (Willian 69), Martinelli (Elneny 83); Lacazette (Nketiah 88).
Unused substitutes: Bellerin, Gabriel, Soares, Nelson, Ryan, Azeez.
Referee: P Bankes (Merseyside).
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