The Blades were cruelly denied a last four spot in the Emirates FA Cup at Bramall Lane on Sunday afternoon.
The home side dominated and pushed back the Gunners for long periods in both halves of a game that was settled by a late Dani Ceballos effort after David McGoldrick had cancelled out Nicolas Pepe's first-half penalty.
Boss Wilder made three changes for the last eight tie against the Gunners, Henderson was eligible again and Egan was available following a suspension. In attack, McBurnie replaced Mousset who was named amongst the substitutes.
United made a positive start and after Xhaka had fouled McBurnie, Norwood's inviting free-kick was inches from finding Egan's back post run. Moments later, Robinson started and almost finished a free-flowing move. The defender played in McGoldrick down the left channel, continued his run and saw a shot deflected wide for a corner.
The corner from the right eventually landed at the back post where Stevens won another, from which United thought they'd taken the lead only for VAR to intervene in the ninth minute.
Norwood's deep centre was headed towards goal by Egan, but Lundstram was adjudged to have applied the finishing touch from an offside position.
Three minutes later, United could have been in front again. Robinson's long throw was misjudged by a retreating Mustafi, but unfortunately for the Blades the ball somehow evaded McGoldrick outstretched leg.
But on 25 minutes, the home side fell behind in harsh circumstances, against the run of play. Referee Tierney deemed Basham had upended Lacazette, who went down easily, just inside the box and after a stoppage for treatment for the Arsenal forward, PEPE fired past Henderson from the spot.
That goal had given the visitors a foothold in the game and Henderson needed to be quickly down at his near post to deny Pepe from making it two after he had combined with Lacazette. The next action of note saw Fleck yellow carded for a late tackle on Lacazette. A further blow for the home side followed as Lundstram was forced off with what looked a shoulder problem and he was replaced by Berge.
As half-time approached it was Arsenal who continued to look a live threat on the break. Henderson palmed away a centre from Maitland-Niles, before Tierney fired wide. At the other end, United worked an opportunity for themselves, ending with Norwood testing Martinez, but it was Arsenal who came even closer moments later as Pepe sent a first time effort just wide from Tierney's low cross and that was the last meaningful action of the first period despite seven minutes of added time.
Like the first-half, it was United on the front foot at the beginning of the second, but Martinez waa equal to McBurnie's header from Robinson's long throw. The Arsenal goalkeeper was then almost caught out by a long punt forward, before United were denied an equaliser despite a VAR check from Norwood's low free-kick, which ended with Egan forcing the ball home.
On the hour, the Blades should have deservedly restored parity, having fashioned the best opportunity of the game, which ended with Robinson crossing to the back post only for Basham to head wide with Martinez scrambling across his goal. Two minutes later, Kieron Freeman replaced Baldock, prior to the visitors making a double change.
With the Blades pressing forward, Robinson was booked for clipping Nketiah as the visitors looked to break, as Sharp took the place of Basham. As the game entered the last ten minutes, it was United throwing everything at Arsenal, but the ball just would drop favourably for McBurnie and then moments later Fleck.
But finally, with three minutes remaining, the ball did bounce the Blades way and MCGOLDRICK forced the ball home past Martinez after Kolasinac and Holding had failed to clear Robinson's long throw. United were now chasing the winner in normal time, but Martinez denied Sharp at his near post after a flurry of bodies had blocked previous efforts from McGoldrick and Norwood.
Five minutes of added time were signalled and it was Arsenal who snatched an undeserved winner on the break, with CEBALLOS sliding the ball past Henderson following a swift counter involving Saka, Nketiah and Pepe and cruelly that was the way it ended.
Blades: Henderson, Baldock (K. Freeman 62), Stevens, Fleck, Basham (Sharp 75), Lundstram (Berge 35), McBurnie, Egan, Norwood, McGoldrick, Robinson.
Unused: L. Freeman, Jagielka, Mousset, Osborn, Moore, Zivkovic.
Arsenal: Martinez, Mustafi, David Luiz (Holding 54), Tierney, Maitland-Niles, Xhaka, Willock (Ceballos 67), Kolasinac, Pepe (Sokratis 90), Lacazette (Nketiah 67), Saka.
Unused: Macey, Bellerin, Smith, Nelson, Aubameyang.