Gregory, who replaced Gary Waddock on Wednesday, included a surprise in his team selection. Highly-rated Australian Nick Ward was dropped to the bench with youngster Stefan Bailey starting in midfield and Martin Rowlands returning to the right flank after injury.
Rowlands looked Rangers' brightest player during a first half in which the home side enjoyed most of the possession.
Hull survived an early scare when Jones robbed David Livermore inside the box and found Rowlands, whose shot was pushed away by keeper Boaz Myhill.
QPR defender Damion Stewart then missed a chance to score when he failed to connect with Lee Cook's free-kick at the far post.
Cook shot wide as Rangers kept the pressure up, although keeper Paul Jones had to be alert to prevent Hull nicking a goal a minute before half-time. Marc Bircham lost out to Livermore whose pass sent Michael Bridges racing towards goal, but Jones sprinted from his line to clear.
Seconds before the interval, more good work from Rowlands almost led to an opening. The Republic of Ireland international breezed past Andy Dawson to cross from the right and Hull defender Michael Turner had to throw himself at the ball to thwart Blackstock at the near post.
Hull made a determined start to the second period and Sam Collins' header from Dawson's corner brought a good save from Jones.
But it was Rangers that broke the deadlock. Blackstock leapt to head Rowlands' lofted free-kick across the face of the Hull goal and Jones bundled the ball home.
Rangers almost went further ahead when Blackstock headed Marcus Bignot's cross over the bar.
But Blackstock made no mistake 10 minutes from time, heading Cook's left-wing delivery past Myhill and into the corner of the net.
The win lifted Rangers off the bottom of the Championship and piled the pressure on Hull manager Phil Parkinson, whose side have now lost six times this season.