The away side thought they had nicked the winning goal when Danny Fox fired in a free-kick against the run of play with 17 minutes left after team-mate Stephen Wright was dismissed in the first half.
But leading scorer Blackstock bravely chased a through ball and rose above the onrushing Keiren Westwood to nod home.
QPR had the better of the first half but, while they enjoyed the majority of the possession, they found little end product.
After seven minutes, Icelandic international striker Heidar Helguson swivelled and shot in the Coventry area but his shot was weak and easily gathered by Westwood in the away goal.
Helguson had another chance nine minutes later when the ball dropped to him on the edge of the area, but the 31-year-old was wasteful again and laced his half-volley high over the bar.
Wayne Routledge soon began to show why QPR shelled out £600,000 in the week as he menaced Coventry down the left flank.
He gave right-back Aron Gunarsson a torrid time and when Routledge past him after 25 minutes, Wright had to come across and foul him on the edge of the area.
Though QPR failed to make the free-kick count, a booking was dished out and that should have calmed Wright down.
But nine minutes later, his high and reckless challenge on Helguson warranted a straight red card from referee Keith Stroud and changed the game's complexion.
In injury time before the interval, QPR managed their first meaningful shot on Westwood's goal when left-back Damian Delaney fizzed a shot that the goalkeeper did well to parry.
After the break, QPR huffed and puffed but still found Coventry hard to break down.
Ten minutes in to the half, Mikele Leigertwood looped over a pass that beat the away side's offside trap and with the goal gaping, Blackstock could only scuff his shot wide left.
With Routledge now on the right, QPR tried to change the angle of attack but the home crowd were getting restless at the lack of real chances.
With just over 20 minutes remaining, Helguson was profligate once again when he failed to poke in Deleney's driven cross.
And those wasted chances cost QPR dearly as when a frustrated Helguson fouled Michael Misfud after losing possession, he conceded a free-kick 30-yards out.
Fox, the left-back who is a set-piece specialist, stepped up and coolly placed his effort inside the right-hand post of Radek Cerny's goal.
Helguson, anxious to make amends, proceeded to miss two more gilt-edged opportunities – one which was sliced out for a throw in.
Luckily his strike partner, Blackstock, was more fortunate and put his head in bravely in the 87th minute while chasing substitute Emmanuel Ledesma's hopeful punt.
He headed in the leveller and the relief was palpable for the home side.
While they took their unbeaten run at home to six games, question marks will remain over their potency up front.