The first attempt on goal arrived on four minutes when City's Alan Sheehan curled a 20 yard shot the wrong side of Paddy Kenny's left hand post.
United had to wait until the 28th minute for their first assault on goal when Phil Bardsley's 20-yard drive was turned away by Marton Fulop with Gary Cahill heading Keith Gillespie's resultant corner just over.
On the half hour mark, Matt Fryatt turned his marker to float an edge of the box shot just wide.
With skipper Stephen Clemence going off injured after 18 minutes to be replaced by Shaun Newton, City made their second substitution on 32 minutes when Collins John came on for Dudley Campbell.
John arrived at the Walkers Stadium on a three month loan from Fulham on the eve of the game in which he made little impact.
Kenny attempted struggled on after receiving lengthy treatment following a collision with his own defender Cahill. Clearly in pain with an injured leg, he hobbled off after 39 minutes to be replaced by substitute keeper Ian Bennett.
Both sides quickened their pace after the restart with Bardsley threatening for the Blades when he drove a 22-yard shot straight at Fulop.
The visitors' enterprise was rewarded on 55 minutes when Bardsley whipped in a cross from the right for Webber to slide in and score at the near post.
The setback prompted Gary Megson to make a tactical switch to a 4-4-2 formation with Bruno N'Gotty making way for Levi Porter.
But it was the Blades who continued to pose the greater threat, going close to doubling their advantage when James Beattie outsmarted Patrick Kisnorbo to fire just over before Cahill headed a Keith Gillespie free kick over the bar.
That was to prove the last significant action in a sterile encounter which ended with Leicester fans chanting "Megson for Bolton," a wish which could soon come true.