Sharp scored with a header and Speed converted the rebound from his own penalty, whilst Elliott Ward was on target for the visitors, also from the spot.
Referee Kettle was forever whistling, awarding two penalties and showing eight yellow cards - all in the second half - as United recorded a second successive league win.
Both teams named unchanged teams after weekend wins and before play commenced Bramall Lane fell completely silent for a minute in tribute to former Blades chairman, Derek Dooley, who sadly passed away last week.
United were forced to kick towards the Kop in the first half and the action in the opening ten minutes was so frantic that it was a surprise that the deadlock was not broken. On six minutes Dann found himself clear in the box and after his initial shot was saved by the Blades goalkeeper, Naysmith gave the Coventry defender a second chance, which was kicked off the line by Speed.
Within a minute the Blades were on the attack and came within a yard of levelling. Sharp beat Marshall but in a difficult position was unable to get enough purchase on his shot and Ward cleared from in front of the goal-line. Beattie looked in a good position to finish off the move but obviously felt he would have been called offside should he have added a vital touch.
After United half-cleared the night's first corner, Mifsud's long range shot was deflected by Danns but Kenny was ideally placed and then Best fired powerfully over the crossbar from 20 yards.
Carney was the instigator of chances after 18 and 19 minutes. He provided the cross for Sharp to get in front of his marker and turn the ball past Marshall but he was denied a first Championship goal by a linesman's flag. Then another delivery from the Australian beat the Coventry goalkeeper but Beattie was pressured at the back post.
Just before half hour mark Best cut in from the left and curled a right-footer just over the angle of post and crossbar which appeared to be the signal for a sudden and heavy downpour of rain, which lasted five minutes.
The frenzied start couldn't continue and the chances slowed as the half progressed. On 36 minutes Beattie fired a 30-yard free-kick just over the crossbar and a minute before the break Best's free-kick hit the wall and Osbourne's follow up was saved by Kenny.
In the one minute of injury-time, Coventry worked the best move of the period. Hughes and Tabb were involved before Thornton's shot was blocked by the legs of Kilgallon and from the resulting corner, Danns was denied by a superb reaction save from Kenny.
Coventry made the brighter start to the second period, to the frustration of the Blades fans and on 50 minutes Kenny made enough vital save, this time at the near post after a shot from Mifsud deflected off Kilgallon.
Thornton's curler was comfortable for Kenny, whilst Blackwell was forced into a change in attack when Hulse replaced Beattie, who appeared to be struggling. Gillespie was also introduced soon after, taking the place of Carney.
United's slow start was forgiven when the opening goal arrived from a popular source on 69 minutes. Geary's shot was blocked but the loose ball fell to Cotterill who, for the second successive game, held a cross up to the back post and SHARP rose above Ward to head home. The Sheffield-born striker's celebrations were wild in front of the Valad Stand and he picked up a booking from the referee.
The action continued and the referee bemused most of the crowd on 78 minutes when he awarded United a penalty. Geary's cross dropped harmlessly over the crossbar but Mr Kettle spotted a foul by Hughes on Sharp. After the protestations subsided, SPEED stepped up to take the penalty and although Marshall blocked the initial effort the midfielder slotted home the rebound with his unfavoured right foot.
Sharp latched on to a mistake by Danns and looked set to net his second but side-footed just wide in a one-on-one situation with Marshall, whilst the Blades were pegged back a minute later.
The man in the middle appeared to level up the penalty count when Morgan clashed with Mifsud. The penalty was generous, at best, and WARD fired powerful beyond Kenny's reach.
The goal set up a close finish for the Blades but it was the home side who did most of the attacking late on. With Marshall off his line, Hulse was well off target with an attempted lob and in injury-time Fox bravely denied Sharp a second from Gillespie's cross.
For the second consecutive game Ehiogu was thrown on to sure up the defence late on and there were cheers for the home side and jeers for the match officials after the final whistle.
Blades: Kenny, Naysmith, Morgan, Beattie (Hulse 57), Cotterill (Ehiogu 90), Carney (Gillespie 64), Speed, Kilgallon, Tonge, Sharp, Geary.
Unused: Stead, Bennett.
Coventry: Marshall, Fox, Ward, Hughes, Doyle, Osbourne, Mifsud, Tabb, Best, Dann, Thornton.
Unused: Hall, Andrews, Ireland, Simpson, Gray.
