It took 17 minutes for either side to create a noteworthy chance and such is Charlton's luck at present that it was inevitable they would go behind when one arrived.
Damiano Tomassi just managed to keep the ball alive on the left wing and fired in a low cross which found Blackstock unmarked seven yards out, the striker made no mistake to claim his eighth goal of the season.
But Charlton hit back on the half-hour mark when Therry Racon arrived unmarked right on cue to slide home Hameur Bouazza's fiercely driven cross.
Sousa introduced Patrick Agyemang at the interval for the woeful Samuel Di Carmine, but it was Charlton who made the more encouraging start to the second half.
Bouazza wriggled to the by-line and squared invitingly for Martyn Waghorn, who was denied what would have been the first goal of his loan spell from Sunderland by Damien Delaney's magnificent block.
Linvoy Primus then volleyed onto the roof of the net after Bouazza's free-kick fell kindly to him.
At the other end Ageymang fired narrowly over after an adventurous run, but QPR failed to impose themselves on opponents short on confidence after Saturday's 5-2 drubbing against Sheffield United.
And the visitors nearly snatched the lead with 15 minutes remaining when skipper Mark Hudson glanced debutant Keith Gillespie's cross narrowly wide.
That miss was to prove costly, as moments later QPR broke up the other end and Hogan Ephraim crossed for Blackstock, who showed Hudson how it should be done by steering his header into the top corner.