Jonathon Douglas put Leeds ahead just past the half-hour with a tidy volley only for Don Hutchison to equalise with a long-range volley on 58 minutes.
Robbie Blake fired into the roof of the net to make it 2-1, with Richard Creswell's drilled shot adding a third.
With eight minutes left Gary McSheffrey missed his spotkick after Michael Doyle had been brought down by Paul Butler.
Coventry boss Micky Adams:
"It wasn't our day. It's all about scoring goals and we have created chances and then been a little bit unfortunate.
"It looked as though we dominated. We played terrific football and frustrated Leeds but it's all about scoring.
"We came here full of confidence and it showed. The players have seen enough to realise it was a good display and we have to take that into the Crewe game."
Leeds: Sullivan, Kelly, Butler, Kilgallon, Harding, Douglas, Derry, Lewis, Healy (Richardson 90), Cresswell, Blake (Hulse 81).
Subs Not Used: Bennett, Wright, Pugh.
Booked: Derry, Sullivan, Kilgallon.
Goals: Douglas 34, Blake 61, Cresswell 80.
Coventry: Fulop, Whing, Page, Shaw, Duffy, Morrell (Jorgensen 73), Doyle, Osbourne (Scowcroft 79), McSheffrey, Hutchison, Adebola (Impey 84).
Subs Not Used: Ince, Heath.
Goals: Hutchison 58.
Ref: C Webster (Tyne & Wear).