Leeds led when Eddie Lewis' corner was flicked on and an unmarked David Healy rifled a low shot home.
Robbie Blake hit the crossbar but Coventry equalised when Adam Virgo sidefooted in from Kevin Kyle's cross.
Douglas pounced when Coventry keeper Andy Marshall could only parry, but Coventry could have snatched a point when Kyle headed against the post.
Coventry boss Micky Adams:
"The name of the game is putting the ball in the back of the net and we've not done that.
"It takes us to go a goal down before we wake from out slumbers and that's
Leeds: Sullivan, Richardson (Westlake 61), Foxe, Rui Marques, Robbie Elliott, Blake (Howson 75), Douglas, Nicholls, Lewis, Healy, Moore (Kandol 73).
Subs Not Used: Warner, Carole.
Booked: Nicholls, Douglas.
Goals: Healy 15, Douglas 53.
Coventry: Marshall, Whing (Currie 68), Page, Ward, Hall, Birchall (McKenzie 55), Osbourne, Doyle, Tabb (Adebola 56), Virgo, Kyle.
Subs Not Used: John, Cameron.
Booked: Page, Whing, Kyle.
Goals: Virgo 43.
Ref: M Pike (Cumbria).