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The hosts carved out an early chance to take the lead when Kevin Davies fired a volley towards goal that Mark Howard struggled to deal with at first, but the keeper recovered in time to smother the ball at the feet of Joe Garner.
They came close again in the 15th minute when Paul Gallagher let fly with a free kick, sending his curling effort narrowly over the bar.
Preston continued to trouble the United defence and had another chance to open the scoring just six minutes later when Davies showed good strength to set up Garner, who couldn't get enough on his header to trouble the keeper.
The visitors thought that they had broken the deadlock shortly after the half-hour mark when Conor Coady put the ball in the back of the net, but the linesman had raised his flag for offside.
The hosts came within inches of taking the lead after the restart when Josh Brownhill fired an effort into the ground, only to see it bounce up and off the post.
Garner was the next to come close for Preston as he latched on to a Chris Humphrey cross, but his strike went narrowly wide.
Neither side could break the deadlock in the closing stages as the match ended goalless, handing the Blades their 10th clean sheet in their last 11 games, while also extending Preston's unbeaten streak to nine.