Billy Davies' side had seen their 19-match unbeaten run brought to a painful end by rivals Derby County last weekend.
But they bounced back by battling their way to three points against the determined Owls at the City Ground.
Blackstock netted the winner in the 80th minute, seven minutes after Luke Varney had drawn the visitors level with a precise finish to cancel out Blackstock's first-half penalty.
Wednesday, perhaps, had taken note of how Derby had achieved their success a week ago and worked hard to ensure Forest could not get into their stride.
The visitors harassed and harried their hosts and, with Forest lacking invention, the game degenerated into a midfield battle.
Ironically, it was through this desire to close down and deny Forest space that Wednesday inadvertently handed the home side the advantage, as skipper Darren Purse conceded a penalty when he handled while trying to shut out a shot from Blackstock, just inside the box.
Referee Trevor Kettle had little hesitation in pointing to the spot - and Blackstock was equally decisive, rifling a powerful shot high to the keeper's left and into the top corner to put Forest ahead in the 24th minute.
The goal sparked Forest into life for the first time, with Nathan Tyson immediately forcing a save from keeper Lee Grant with a low, driven shot from range and Earnshaw sending another shot over.
But the Owls also found a way through the Forest defence for the first time, with Luke Varney, the on loan Derby striker, seeing an angled shot deflected wide by Kelvin Wilson, when he should perhaps have levelled.
Forest came close to adding to their advantage when Robbie Earnshaw bent a precise 20-yard free-kick over the wall and towards the top corner, with Grant saving well with his fists.
It was through a free-kick that Wednesday almost forced an equaliser four minutes into the second half, as Darren Potter saw his driven shot take a deflection off the wall and loop onto the bar.
Chris Cohen saw a long-range effort deflect wide of the post for a corner, while Owls full-back Frank Simek came close with a rising shot that flashed narrowly wide.
A double substitution from manager-of-the-month Alan Irvine added fresh energy to Wednesday, as he brought on Leon Clarke and Etienne Esajas, who played a part as the Yorkshire side found an equaliser.
It was his ball, fed into the box, that pin-balled around until falling kindly for Varney to power low into the back of the net from 12 yards.
Wednesday were level for only seven minutes however, as Forest hit back to take the lead again.
Cohen bent an in-swinging free-kick into the goalmouth where Blackstock saw his header well saved - but was well-placed to sweep home the rebound for his second goal of the game.