Draws against Millwall and Wolves had seen Neil Warnock's side surrender top spot in the Coca-Cola Championship this week, while Blades fans will also be worried by speculation linking their manager with the vacancy at Portsmouth following Alain Perrin's sacking at the Premiership club on Thursday.
And the problems continue to pile up for the Blades as Leicester took advantage of the visitors' current blip.
Iain Hume and Ryan Smith had the hosts in cruise control before Steve Kabba, linked with a move away from Bramall Lane in January, shrugged off speculation about his future to give United a glimmer of hope.
But Elvis Hammond sealed the points before Hume scored his second and Webber scored in a frantic finish.
Leicester manager Craig Levein made two changes with Hume and Nils-Eric Johansson in for Mark de Vries and Richard Stearman, while Vincent Pericard replaced Neil Shipperley in Warnock's starting XI.
The Blades had gone two Championship games without a win for the first time this season and, desperate to end that run, almost got off to a flier with Webber heading narrowly wide after just 26 seconds.
But Hammond went even closer at the other end five minutes later when his header hit the crossbar before he set up Hume for the opener. The former Fulham striker got his head to Smith's cross and Hume lashed the ball home from close range with 11 minutes gone.
The visitors had not fully recovered when Hume then turned provider with a quarter of an hour on the clock, creating space on the right before crossing for on-loan Arsenal winger Smith to double the advantage with a header.
The Foxes continued to send dangerous crosses into the United penalty area and Hume forced Paddy Kenny into a save from another Smith centre.
The visitors enjoyed their best spell in the closing stages of the first half but Leicester went in two goals to the good.
Warnock withdrew former Leicester man Keith Gillespie at the break and the tactical switch paid off after 51 minutes when his replacement Kabba halved the deficit with a tap-in following good work from Webber on the right.
Leicester refused to buckle and when Hammond raced clear at the other end it took a brave stop from Kenny to keep the Blades in the match.
The game burst into life after Kabba's strike and Derek Geary was only denied an equaliser by an impressive save by Rab Douglas before Kenny produced an even better stop at the other end, again foiling the lively Hammond from close range.
But the Leicester striker would not be put off and put the result beyond doubt with just over quarter of an hour left, beating Kenny with a cool finish into the corner with Smith again involved in the build up.
Hume doubled his own tally with another powerful finish in time added on but there was still time for Webber to bundle home a header.