Nick Blackman's late goal - his first in the league for the Blades - secured a point at the Ricoh Arena on Tuesday night.
The Blades were the better side and dominated the first half but looked like tasting defeat when Stephen Elliott gave Coventry the lead just after the hour.
But with six minutes remaining, Blackman turned in Shaun Miller's cross to secure a point - no less than Danny Wilson's side deserved.
Chief Wilson made just one change to his team with left-back Hill replacing Williams, who dropped to the substitutes bench, where he was joined by the fit-again Flynn. Wearing the new black and orange away kit competitively for the first time, the Blades kicked off to a few verses of songs from the Unitedites packed in one corner of the Ricoh Arena.
Referee Tierney's first act was to book Hill for a late challenge on Barton on seven minutes, whilst the initial assaults on Coventry's goal came as a result on Cofie's pace and his cross, after a fortunate bounce, was cut out by Wood as Blackman looked ready to pounce.
Wood again saved his team on 11 minutes when Coventry were caught out by a quick Quinn set-piece, which found McDonald in space - the Scot cut inside and beat goalkeeper Murphy with his shot but Wood kicked off the line. The home side appeared to struggle to come to terms with United's formation early on, which included Quinn enjoying the freedom of an advanced role in support of Cofie and Blackman.
United dominated the first 20 minutes and another chance went begging when Maguire headed Quinn's corner wide, whilst long-range efforts from McAllister and Cofie were deflected wide. Coventry's only threat of the first half hour was a Baker cross, which saw Howard punch to safety.
Before the break, McMahon's 30-yard free-kick was curled into the arms of Murphy, whilst Coventry appealed for a penalty when McDonald went down under McAllister's challenge but the referee was not convinced and the sides left the field at half-time with all to play for in the second period.
The Blades were first to show attacking intent in the second period and in the first ten minutes McAllister almost got on the end of McDonald's cross and Quinn chipped over the crossbar. For the home side, McDonald and Elliott both connected with crosses but failed to test Howard.
However, Coventry went extremely close to opening the scoring just before the hour. Maguire conceded a debatable corner and from Baker's delivery, Malaga's header was kicked off the line by McDonald and the Blades scrambled the ball into the arms of Howard.
Wilson threw on Miller but United went behind with the next home attack, with 62 minutes on the watch. A routine long ball was allowed to bounce and ELLIOTT held off Maguire before firing high into Howard's goal.
In response, McAllister fired over after Miller had held up McMahon's pass, whilst Blackman's shot was also too high as United built up well through the middle but time was running out.
Malaga went close to adding a second, heading Baker's free-kick just wide, before the Blades struck with a quality goal on 84 minutes. United won back possession after Maguire was robbed and a move with pace down the left resulted in Miller firing across goal and BLACKMAN throwing himself at the ball at the back post, directing it past Murphy. The goalscorer whipped off his shirt and sprinted off to celebrate with the fans - earning a booking in the process.
Miller could have had a goal himself had the ball dropped nicely for him from Quinn's cross, whilst from McDonald's cross in injury-time Malaga almost turned the ball past his own goalkeeper.
In the three minutes of added time, United looked the more likely to push for a winner but a hard-earned away point was confirmed by referee Tierney's whistle.
Coventry: Murphy, Hussey, Malaga, Wood, Brown, Baker (McSheffrey 88), Kilbane, Barton, Jennings, C. McDonald, Elliott (Ball 85).
Unused: Dunn, Edjenguele, Daniels, Willis, O'Donovan.
Blades: Howard, Maguire, Hill, Doyle, Blackman, K. McDonald, Collins, Cofie (Miller 61), Quinn, McMahon, McAllister.
Unused: Flynn, Harriott, Philliskirk, Ironside, Long, Williams.