The Blues took a first-half lead when Bruno N'Gotty - who had earlier gone close - headed past Paul Jones.
DJ Campbell had a goal ruled out for handball, while David Dunn and Neil Danns both saw shots deflected wide.
Campbell hit the post before Bendtner was dismissed for two quick bookings, but the Blues sealed the win when Cameron Jerome lobbed in at the death.
Birmingham assistant boss Eric Black on being top of the Championship
"It's nice to be there. We've now got to focus on what we are doing and just see what the other teams do.
"The players answered the question of whether they have character.
"They are starting to get the idea of what is needed on a week-to-week basis and are getting rewards, even though they are not firing on all cylinders."
QPR: Paul Jones, Rose, Rehman (Baidoo 74), Stewart, Milanese, Oliseh, Bircham, Ward, Cook, Nygaard, Blackstock (Ray Jones 45).
Subs Not Used: Cole, Bailey, Kanyuka.
Birmingham: Maik Taylor, Johnson, Jaidi, N'Gotty, Larsson, Danns, Dunn (Kilkenny 76), Muamba (Martin Taylor 90), McSheffrey, Campbell (Jerome 71), Bendtner.
Subs Not Used: Doyle, Forssell.
Sent Off: Bendtner (68).
Booked: Johnson, Dunn, Bendtner.
Goals: N'Gotty 23, Jerome 90.
Ref: P Melin (Surrey).