Hull were under pressure but could have led if QPR keeper Paul Jones' had not saved from Michael Turner's header.
Rangers broke through on the hour as Jones tapped in his first league goal after being set up by Damion Stewart.
And Blackstock sealed the victory as he headed home after Lee Cook supplied a superb curling cross.
Hull manager Phil Parkinson
"We looked off the pace and when that happens you have to stick together and try to grind out a draw. "If we'd defended the first goal we could have come in with a draw.
"But that's the first game for a while we haven't looked a goal threat. We didn't threaten the opposition goal enough to say we deserved anything."
QPR: Paul Jones, Bignot, Rehman, Stewart, Rose (Kanyuka 45), Rowlands, Bircham (Ward 64), Bailey (Lomas 64), Cook, Ray Jones, Blackstock.
Subs Not Used: Royce, Baidoo.
Booked: Ray Jones, Rehman, Paul Jones.
Goals: Ray Jones 60, Blackstock 80.
Hull: Myhill, Mills, Turner, Collins, Dawson, Fagan, Livermore (Marney 75), Ashbee, France (Yeates 67), Parkin, Bridges (Forster 67).
Subs Not Used: Duke, Thelwell.
Booked: Collins, Mills, Livermore.
Att: 11,381
Ref: D Deadman (Cambridgeshire).
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