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Unai Emery’s side had not been beaten in any competition since their 3-1 loss to Liverpool on Aug 24, but they missed out on the chance to move up to third as the hosts earned a deserved victory.
Lys Mousset poked home the winner from close range on his first league start for the Blades after Nicolas Pepe wasted a gilt-edged chance for Arsenal earlier in the first half.
"For the club to host a game like this, the magnitude of it - to play well and get a win is massive,” Sheffield United manager Chris Wilder told Sky Sports.
"We came under pressure in the second half but we limited them to a few chances and we backed up a good performance with a good result.”
The result leaves Arsenal in fifth place on 15 points, two behind Leicester City and Chelsea, while Sheffield United moved into ninth on 12 points.
Arsenal came into the game with five wins in their last six games in all competitions, while the Blades had lost their last three home games in a row.
The defeat continued a poor run of away form for the Gunners, who have now picked up just two points from their last four league matches on the road.
Emery was left unhappy with the result and believed his side should have been awarded a penalty in the first half for a shirt pull by John Egan on Sokratis Papastathopoulos, which was waved away by referee Mike Dean.
"With VAR, the foul on Sokratis should have been reviewed," said the Arsenal manager.
"It was clear but we have to accept it. We did not deserve to lose and we will think about where we can improve."
Pepe squandered a glorious chance to give Arsenal the lead midway through the first half when he got on the end of a Sead Kolasinac cross but miscued his finish horribly from six yards out.
Mousset punished the visitors’ wastefulness when Jack O’Connell headed a corner into his path for the striker to bundle in from close range after half an hour.
Granit Xhaka connected well with a half-volley on the brink of half time but was denied by a flying save from Dean Henderson, and after the break Arsenal substitute Dani Ceballos fluffed a volley from a promising position to give the goalkeeper a comfortable save.
United’s defence held firm and the home side threatened to double their lead through John Fleck, who hit a rasping shot into the side netting before striking a swerving effort from distance which had to be gathered at the second time of asking by Bernd Leno.