Sheffield United's narrow victory means Coventry are now without a win in their last eight games away from home.
Billy Sharp netted his first league goal for the Blades on 69 minutes when he headed home David Cotterill's cross.
With 12 minutes to go Stephen Hughes fouled Sharp in the box. Gary Speed's spot-kick was saved by Andy Marshall but he followed up to net the rebound.
Coventry pulled one back from the spot when Elliott Ward scored after a foul on Michael Mifsud, but it was too late.
Sheffield United manager Kevin Blackwell:
"All credit to Billy - he's a Blade through and through so I can only imagine the pressure he was under.
"He's worked his socks off and even when things haven't been going right for him he's shown great bravery by continually getting in the box.
"We've not won at home for a while now and we had to break that hoodoo."
Coventry manager Chris Coleman:
"I think their first goal was a push on Isaac Osbourne and their penalty was very soft. Our penalty was also soft so I think the ref tried to level things.
"I am a great believer that things even themselves up in a season but it does not make the result any easier to take.
"We have to get things right away from home but this display was worlds away from the second half at Scunthorpe."
Sheff Utd: Kenny, Geary, Morgan, Kilgallon, Naysmith, Carney (Gillespie 64), Tonge, Speed, Cotterill (Ehiogu 90), Sharp, Beattie (Hulse 57). Subs Not Used: Bennett, Stead.
Booked: Sharp, Hulse, Morgan.
Goals: Sharp 69, Speed 78.
Coventry: Marshall, Dann, Ward, Osbourne, Fox, Tabb, Stephen Hughes, Doyle, Thornton, Mifsud, Best. Subs Not Used: Ireland, Hall, Andrews, Simpson, Gray.
Booked: Ward, Tabb, Stephen Hughes, Fox, Osbourne.
Goals: Ward 81 pen.
Ref: Trevor Kettle (Rutland)