Claus Jorgensen netted with a diving header from Gary McSheffrey's cross before Dele Adebola added a brace.
He cut in from the right to fire past Simon Royce at the near post and got a second after Dominic Shimmin sliced Jamie Scowcroft's cross on to the post.
Shittu saw a straight red after pulling back Adebola, who was denied a treble when Royce saved with his knees.
QPR boss Ian Holloway:
"Coventry were like lions and we were like sheep. You could tell they really wanted it whereas we were really awful out there.
"I had seven first-team players out injured but my lot should have made a better fist of it than that, especially given all the preparation we did.
"I thought Adebola was the man of the match, whether or not he did go down like a pansy for the sending off."
Coventry: Bywater, Duffy, Page, Heath, Hall, Flood (Morrell 73), Jorgensen, Doyle, Scowcroft, Adebola (Osbourne 87), McSheffrey (Wood 77).
Subs Not Used: Ince, Williams.
Booked: Heath, Adebola, Hall, Duffy, Flood.
Goals: Jorgensen 11, Adebola 24, 44.
QPR: Royce, Bignot (Ukah 66), Shittu, Shimmin, Rose, Ainsworth, Gallen, Bircham (Bean 66), Brown (Milanese 55), Moore, Furlong.
Subs Not Used: Miller, Baidoo.
Sent Off: Shittu (54).
Booked: Shimmin, Bignot, Milanese.
Ref: A Leake (Lancashire).