VIDEO: Blades 1 Oldham 0 - David Dunn: We were unlucky
United went ahead through Matt Done, who had scored for the Blades when the sides met in the league at Boundary Park in October, and then had Che Adams sent off causing the visitors to increase the pressure, particularly in the latter stages.
Oldham had hit the post in the first half - ex-Blade Danny Philiskirk coming close, then Jake Cassidy headed down and over the bar when well placed in what was the Latics best chance of the second period.
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And Dunn felt his side had done enough to earn a replay.
He said: "We showed the battling qualities you need to come to a place like this against a really good side. I thought we were unlucky not to get at least something out of the game.
"I thought we had probably the better chances - we hit the post in the first half and then Cass' header was a big chance for us."