But Unai Emery and his side may have reason to feel hard done by following the result.
Arsenal started the game off as the brighter of the two teams and could have had a penalty in the sixth minute.
Sokratis Papastathopoulos was in a great position to head a corner at goal but appeared to be tugged down by John Egan.
However, Mike Dean thought otherwise and waved away his protests.
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VAR wasn't even consulted, despite replays showing Sokratis' shirt was blatantly pulled by the Sheffield United player.
Arsenal then should have taken the lead 15 minutes later.
Sead Kolasinac played in a brilliant cross from the left-hand side, giving Nicolas Pepe a golden opportunity from just five yards out.
But the Ivorian winger couldn't make any contact. It was a sitter and he had to score.
And Arsenal were made to pay as they fell behind shortly after.
Oliver Norwood's deep cross was headed back by Jack O'Connell and on hand to convert was Lys Mousset, who tapped the ball in from a few yards out to give his side the lead.
Arsenal battled back well though and had more penalty shouts waved away five minutes later.
Bukayo Saka drove into the box and went down under pressure from Egan, only to be shown a yellow card for diving.
Replays showed that there was a little contact, but Saka did look as if he went down too easily.
Freddie Ljungberg was also booked following the incident.
In the dying moments in the first half Granit Xhaka went close with a speculative long-range effort which was well saved by Dean Henderson.
Emery sent Dani Ceballos on at half-time and he had Arsenal's first chance of the second half.
Saka's cross found it's way to the Spanish midfielder, but his tame effort was comfortably saved by Henderson.
Fleck then went close on two occasions: he lashed a good effort into the side netting, before his long-range strike was comfortable for Bernd Leno.
Alexandre Lacazette was then called upon to help salvage something from the game and Arsenal threw everything at their opponents in the final 20 minutes.
Pepe, Kolasinac and Calum Chambers all had chances late on but Arsenal could not find a way past Henderson and thus missed the chance to move into the Premier League top four.
They remain in fifth, two points behind Chelsea in fourth.
Sheffield United move into the top half in ninth, having accumulated 12 points from their opening nine games.News Now - Sport News