The on-loan Leicester striker shot home on 29 minutes after Coventry failed to deal with Jermaine Wright's corner.
David Healy doubled the lead in the second half, latching on to a long ball from Wright and beating Scott Shearer.
Gary McSheffrey pulled one back with an acrobatic finish eight minutes from time but Leeds held on despite Clarke Carlisle's dismissal for two bookings.
Leeds boss Kevin Blackwell: "We had a very young side out there, a very green side, and that meant I needed Sean Gregan to have a big game because of his experience.
"Come the summertime, if I'm still in a job, I hope I can get some backing from the board to add three or four quality players to what we already have.
"I think we would then have the basis of a very good team for the future."
Coventry: Steele, Carey, Williams, Shaw, Giddings (Staunton 68), Johnson (Barrett 27), Doyle, Hughes, McSheffrey, Adebola (Wood 45), John.
Subs Not Used: Shearer, Osbourne.
Booked: Carey.
Goals: McSheffrey 82.
Leeds: Sullivan, Richardson, Carlisle, Kilgallon, Pugh, Lennon (Spring 83), Wright, Gregan, Walton, Healy, Blake (Joachim 79).
Subs Not Used: Carson, Ricketts, Einarsson.
Sent Off: Carlisle (84).
Booked: Kilgallon, Healy, Blake, Carlisle.
Goals: Blake 28, Healy 65.
Att: 19,084.
Ref: N Miller (Co Durham).