As against Preston North End a week before, Neil Warnock's side demonstrated patience to strike late if necessary and David Unsworth converted a spot-kick awarded for Richard Duffy's trip on Alan Quinn.
"That's the fifth time in six games I've scored on debuts," said the defender, newly signed on a three-year deal from Portsmouth. "I've always taken penalties and always felt confident taking them." To which their other scorer, Steve Kabba, smiled: "David has not missed one in his career, so he says. But I'm taking the next one if I'm on the pitch."
Kabba, having converted from the spot against Leicester City on the opening day, was off with cramp at the conclusion of this lively contest and on at the outset because Danny Webber hurt his calf in the warm-up. He grasped his opportunity with an emphatic angled finish on the run three minutes after James Scowcroft had clipped Coventry ahead midway through the first half.
Warnock was pleased with two summer recruits from south London, Neil Shipperley and Paul Ifill. The manager has been able to make genuine investment in his side after Sheffield's status as a selling club for several years.
Coventry's date with Southampton tonight will be only their second home game in six this season. Their manager Micky Adams is relishing that prospect after accusing "Sheffield United people" of influencing the referee Colin Webster at half-time.
Adams would not elaborate and admitted Heath's two yellow-card challenges were careless. He said: "The referee has been put under pressure and it's normally the away side who suffer."
Goals: Scowcroft (24) 0-1; Kabba (27) 1-1; Unsworth pen (88) 2-1.
Sheffield United (4-4-2): Kenny; Bromby, Short, Morgan (Gillespie, 74), Unsworth; Ifill, Jagielka, Montgomery, Quinn (Kozluk, 90); Shipperley, Kabba (Tonge, 81). Substitutes not used: Barnes (gk), Nalis.
Coventry City (4-4-2): Bywater; Duffy (John, 90), Heath, Page, Hall; Flood (Morrell, 81), Doyle, Osbourne, McSheffrey (Whing, 70); Adebola, Scowcroft. Substitutes not used: Ince (gk), Woods.
Referee: C Webster (Tyne & Wear).
Booked: Sheffield United Morgan, Short; Coventry City Heath, Doyle, Page.
Sent off: Heath (70).
Man of the match: Ifill.
Attendance: 17,739.Reuse content