New Blades boss Kevin Blackwell, who replaced Bryan Robson last week, received a standing ovation from the Bramall Lane crowd before kick-off as the home side went in search of a hat-trick of Premier League scalps in this year's competition.
Middlesbrough were aiming to reach a third successive FA Cup quarter-final and started with Mido, who has been out for the last three weeks, alongside Jeremie Aliadiere in attack with record signing Afonso Alves on the bench.
It was a typical cup tie right from kick-off with both sides fully committed and the game played at a frenetic pace.
The visitors struggled to settle and Matt Kilgallon's smartly struck shot was well saved by Mark Schwarzer.
Billy Sharp failed to connect with Derek Geary's cross and Jonathan Stead sent his downward header just wide as the home side continued to press, while at the other end efforts from Stewart Downing and Aliadiere were easily saved by Kenny.
As the half drew to a close, David Wheater was lucky to escape with just a booking after dragging back Sharp when the striker raced through and in stoppage time Beattie struck the post from a well-rehearsed set-play.
Beattie and Michael Tonge pretended to run into each as they shaped to hit the free-kick, but the former Southampton and Everton striker saw his curling shot crash against the post.
The visitors came to life in the second period, but only after Stead had tested Schwarzer from outside the box.
Mido was denied by Kenny when he tipped the Egyptian's acrobatic overhead kick over the bar and from the resulting corner Wheater's powerful header was turned over by the Blades goalkeeper
Downing then flashed a brilliantly struck volley wide from Mido's pinpoint pass and Fabio Rochemback also went close with an effort from outside the box as Boro took control.
Just like their hosts in the first period, the visitors failed to take their chances and Blades substitute Chris Armstrong flashed the ball over the bar after another well-worked free-kick.
United had appeals for a penalty turned down late on as George Boateng struck the ball against his own arm, but referee Chris Foy waved away the protests.
And with two minutes remaining Pogatetz could have snatched it for Boro but his header was cleared off the line.
Sheffield United manager Kevin Blackwell:
"I was delighted with their attitude, their application and the things that I've asked them to do they've tried to do.
"We took on a Boro side you are in good form at the moment and that just shows you the level of performance.
"I thought we worked exceptionally hard and it was one hell of a Cup tie in terms of effort and spirit."
Middlesbrough manager Gareth Southgate:
"Because we're the Premier League side I think we would have been favourites from the off.
"But we've seen what Sheffield can offer and they've got a lot of Premier League experience.
"The job's not done, but we've seen a lot of teams go out and it's good to still be in the hat."
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Report: Sheff Utd 0-0 Middlesbrough
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