Bendtner scored the game's only goal in the 15th minute when he headed home from Gary McSheffrey's corner.
McSheffrey had already had a free-kick cleared off the line by that stage, while the striker also hit the bar.
Richie Cresswell was unlucky not to level when replays hinted his shot had crossed the line in the second half.
Leeds manager Dennis Wise:
"We have told the players where we feel we can get the points we need to keep us up and I think they started to realise what we need to do is still more than possible.
"We have got to look at things in a positive manner and I would be worried if we were not creating chances, but we are, and we should have had at least a point out of Birmingham.
"If we had got video evidence to call on we would be at least a point better off now but we have to work with what we have got.
"Cresswell's effort was a goal, plain and simple."
Birmingham: Doyle, Kelly, N'Gotty, Martin Taylor, Sadler, Larsson (Gray 84), Muamba (Nafti 81), Clemence, Bendtner, Vine (Jerome 76), McSheffrey.
Subs Not Used: Maik Taylor, Campbell.
Goals: Bendtner 15.
Leeds: Stack, Richardson, Rui Marques, Heath, Lewis, Howson (Moore 60), Nicholls, Douglas, Blake (Armando Sa 57), Healy (Johnson 67), Cresswell.
Subs Not Used: Einarsson, Carole.
Ref: R Styles (Hampshire).