Bramall Lane reaction: I don't think it was a red card, says Blades chief Wilder
Jamie Paterson put City ahead just before the break with a stunning strike, only for Leon Clarke to equalise shortly after the restart with another fine finish.
Mark Duffy twice hit the woodwork for the hosts, while Billy Sharp hit the top of the crossbar and then had a header turned onto the bar by goalkeeper Frank Fielding.
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Hide AdThe Blades were reduced to 10 men in the 59th minute when John Fleck was shown a red card following a reckless challenge on Korey Smith.
But despite going on to have the better chances, Sheffield United were beaten when Flint snatched a winner with a far-post finish from Bobby Reid’s cross.
Johnson said: “It was a great win, first and foremost, and I’m delighted with the points.
“I thought Sheffield United were outstanding and they were certainly the better side for the first 55 to 60 minutes. I had to change the shape three times and that was due to Sheffield United’s relentless quality.
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Hide Ad“My boys stuck in. It was about dealing with the atmosphere and dealing with the quality.
“We got a bit of fortune with the sending-off. It probably was a sending-off and once they went down to 10 men, I thought we controlled the game.
“The boys have been fantastic. We didn’t have a great away record last season and maybe last year we would have caved under the relentless pressure.
“Korey Smith is not in great shape because he’s struggling to weight-bear and he’s got a nasty gash.”
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Hide AdSheffield United manager Chris Wilder said: “It’s a cruel game at times. I didn’t think we deserved the defeat. I thought we did more than enough to win against a really good side that’s going well.
“I was delighted with the reaction from last Saturday (a 3-1 defeat at Millwall). I think we showed everybody in this division that we’re a decent side when we play as I know we can and we’re a match for anyone.
“Things aren’t really going for us but we’ve just got to keep going. Sometimes fortune doesn’t favour the brave.”
On the sending off, Wilder added: “The game has gone if you can’t tackle like that now. That was just a proper tackle and I don’t think it deserves a red card. Maybe the referee has been watching too many Premier League games.
“I can’t be disappointed with the performance because performance levels were up there with what I expect from the players.”