And the Saints had reason to leave Loftus Road feeling aggrieved after defender Oliver Lancashire was controversially sent off on his debut.
Rangers made the perfect start, going ahead after a minute when the Saints defence failed to clear Gavin Mahon's long throw and Blackstock had time to steady himself and volley home from ten yards out.
Southampton lost Lee Holmes, who limped off on 22 minutes, and they then had Lancashire harshly dismissed following a challenge on Damien Delaney.
Lancashire seemed to make a genuine attempt to win the ball yet was shown a straight red card.
That left Southampton facing an uphill struggle and they were prevented from going further behind by keeper Kelvin Davis, who did well to tip over Lee Cook's rasping shot.
Davis then produced a brilliant stop, diving to his right to parry Blackstock's diving header from Cook's cross.
And just before half-time, Blackstock was denied by a combination of Davis and the woodwork.
Delaney galloped down the left, played a one-two with Mikele Leigertwood and pulled the ball back for Blackstock, whose effort hit Davis and then the post.
Rangers looked to be in control but Southampton equalised seven minutes into the second half.
Adam Lallana burst into the area, collected Simon Gillett's pass and slotted the ball past R's keeper Radek Cerny and into corner of the net.
But Rangers went back in front nine minutes later, when substitute Martin Rowlands' free-kick was nudged home by centre-back Damion Stewart.
And Blackstock's second goal sealed a victory that took QPR up to fourth.
Cook released Patrick Agyemang and after the striker's shot was blocked by Davis, Blackstock fired the loose ball into an unguarded net.
There was still time for Blackstock to set up Agyemang, who collected his strike partner's pass and shot past Davis to register his first goal of the season.