A late goal prevented United's improved second half performance earn a point in Friday night's encounter at Bramall Lane.
Dave Kitson's scored from a Barry Robson corner as United battled back from an early Leon Clarke goal but the Coventry striker added a second with three minutes to go.
Robson and Jonathan Forte both impressed as substitutes but the Blades remain without a league win in 2013.
Boss Wilson opted to name new arrivals Forte and Robson on the bench but there were recalls for Collins and Flynn, who took the places of Westlake, who dropped to the bench, and Premiership-bound Blackman.
The line-up of the team saw Higginbotham start at left-back for the Blades for the first time, allowing Collins and Maguire to re-acquaint in the heart of the defence. It was United's rearguard that were tested first, Coventry winning a succession of corners and Baker wasting a good opportunity at the back post from Elliott's cross.
The Kop attempted to lift the home side and Higginbotham made a couple of timely interventions but the Blades fell behind on 14 minutes. Porter gave away a cheap throw and from a resulting Baker cross, CLARKE's effort deflected off Maguire and found the net via the underside of the crossbar.
McSheffrey shot wide after McMahon's mistake and United's only attempts of the first half hour came from Kitson, his first a header from 15 yards and his second a long-range shot, which was blocked. McMahon picked up a yellow card on the half hour, referee Sarginson indicating a series of fouls by the right-back, and Kitson was the second booked for a lunge at Baker.
The later stages of the half saw United operate more in Coventry's territory but without seriously hurting the visiting side's back four.
Murphy fired over a half-chance early in the second period but Long had to make a save from Edjenguele's header on 50 minutes to ensure the Blades did not fall further behind.
Forte was introduced for his second debut on 54 minutes, replacing Porter, and it gave the crowd a lift, three sides of S2 finding their voice. The substitute soon registered United's first effort on target, shooting at goalkeeper Murphy, who gathered at the second attempt, after Doyle had challenged from a Higginbotham cross.
Long had to save an effort from distance by Baker and McMahon blocked from McSheffrey but the Blades were attempting to mount a spell of pressure. On 67 minutes there were huge shouts for a penalty but the referee said no. Higginbotham's forward ball was headed down by Kitson and McDonald took a touch before he appeared to be held back by Adams, just yards from goal.
Robson was introduced with just under 20 minutes to go and he was influential in United levelling. The debutant's first touch was to deliver a corner, from which KITSON powerfully headed past Murphy from six yards. Kitson volleyed wide soon after as United forced the visitors back.
Forte hooked one wide as the game entered the final ten minutes, whilst Robson was offside after an enterprising run from Flynn. McDonald was booked for a tired challenge and United's games crumbled on 87 minutes. Kitson's pass was intercepted by Moussa and although his effort was parried by Long, CLARKE was ideally positioned to slot home the rebound.
It could have been worse following a break from a Blades corner but Long saved with his feet from Thomas. Five minutes of added time brought hope - Robson's shot was blocked and Doyle fired over - but the last action was Long saving from Jennings as a third consecutive home defeat was confirmed soon after.
Blades: Long, Higginbotham, Maguire, Flynn, Doyle, Porter (Forte 54), McDonald, Kitson, Collins, Murphy (Robson 71), McMahon.
Unused: Westlake, Cresswell, Ironside, Coyne, De Girolamo.
Coventry: Murphy, Baker, McSheffrey (Fleck 74), Jennings, Elliott (Thomas 69), Clarke, Christie, Wood, Edjenguele, Moussa, Adams.
Unused: Clarke, Cameron, Dunn, Barton, Ball.