Rangers striker Blackstock was unable to convert a number of opportunities and both Kaspar Gorkss and Matteo Alberti also missed golden chances to score for the home side.
Blackstock should have netted after just eight minutes when he beat Matthew Kilgallon to collect Mikele Leigertwood's long ball only to shoot straight at keeper Paddy Kenny.
Blackstock had another effort tipped over by Kenny and also fired wide after been found by Samuel Di Carmine's flick-on.
United threatened early in the second half and Nick Montgomery had a shot parried by QPR keeper Radek Cerny, who also did well to deny Danny Webber.
But Rangers had the better chances and Blackstock again went close when he headed wide from Leigertwood's cross.
Then came a farcical scramble in the United box, during which Rangers somehow failed to score.
R's midfielder Jordi Lopez mis-hit the ball towards Di Carmine and the Italian produced an equally woeful sliced shot that fell to Blackstock, whose weak header was pushed out by Kenny.
Gorkss should have buried the loose ball but inexplicably managed to miss the target.
Alberti was just as culpable, side-footing over from 10 yards out after being picked out by Blackstock's left-wing cross.
Rangers' wastefulness was almost punished in the closing minutes when Cerny produced a save to thwart substitute Craig Beattie from close range.
A battling draw is a decent result for the promotion-chasing Blades, but does little to help QPR's flagging bid to reach the play-offs.
Rangers are without a victory in seven matches and have not won at home since December.