The Reds had looked to be heading for defeat after relinquishing the first half lead given to them by Billy Sharp.
But Blackstock sent the visiting fans wild by coolly firing past Matt Gilks in the 90th minute to extend Forest’s unbeaten run to four games.
It was no more than they deserved after looking so comfortable for long periods after Sharp had edged them in front in the 25th minute.
But two goals in the space of five second half minutes, from Elliott Grandin and Gary Taylor-Fletcher, threatened to ruin Forest’s night – before Blackstock’s late, late show.
Boss Sean O’Driscoll was forced to make one change to his starting line-up with Radi Majewski replacing Adlene Guedioura, who began a two-match suspension following his sending-off against Cardiff on Saturday.
Blackstock, available again after serving a three-game ban, was named among the substitutes, along with Jermaine Jenas, who had not been involved at the weekend.
Blackpool, who included former Reds loanee Isaiah Osbourne in their starting XI, gave Forest a fourth minute fright as full back Stephen Crainey fired against Lee Camp’s right hand upright after playing a one-two with Thomas Ince.
The home side survived appeals for a penalty moments later as Chris Cohen went down in the area under a challenge from Osbourne.
An offside flag spared Simon Cox’s blushes as he had blazed over the bar from an unmarked position 12 yards out from an Andy Reid cross from the left.
But Forest’s magnificent travelling support didn’t have to wait too much longer for something to celebrate as Sharp forged the breakthrough.
The on-loan striker forced a sprawling save from Gilks after a speedy counter-attack and when Greg Halford’s left-footed shot from the resultant corner spooned into the air, Sharp reacted quickest and provided a neat finish to beat Gilks.
The home fans were growing increasingly frustrated with the performance of referee Eddie Ilderton and their mood wasn’t helped when he waved away appeals for a free-kick on the edge of the area when Ince went down under a challenge from Halford.
Forest were forced to make a change shortly before the interval as Brendan Moloney replaced Daniel Ayala.
And the substitute played a key role as the visitors went close to extending their lead on the stroke of half-time. Sharp sprang Blackpool’s offside trap to get on the end of Moloney’s ball forward but his shot was deflected behind by desperate Blackpool defending.
Forest started the second half brightly and a neat interchange involving Cohen and Majewski resulted in former Mansfield man Alex Baptiste diverting the Polish international’s cross over his own bar.
Reid, who had an unhappy six-month spell at Blackpool during their Premier League season, almost silenced the home crowd with a long-range free-kick in the 57th minute that flew just inches wide.
Forest looked comfortable but Blackpool levelled 20 minutes from time, as Grandin made the most of hesitant defending to power a header past Camp from Matt Phillips’ right-wing cross.
Things went from bad to worse when Taylor-Fletcher pounced to fire past Camp after Forest had failed to clear on the edge of their area.
O’Driscoll introduced Jenas and Blackstock to the action as Forest went in search of the equaliser their performance deserved.
Sharp was guilty of wasting a half-chance as he sent a left-footed drive wide of the target from an inviting position but Forest had the last laugh.
Reid showed great composure as he picked out Blackstock in the area and as the Blackpool defence waited for an offside flag, the striker calmly beat Gilks to earn Forest a valuable point.
Forest: Camp, Halford, Ayala (Moloney 44'), Collins (c), Harding, Gillett (Blackstock 81'), Cohen, Majewski (Jenas 77), Reid, Cox, Sharp.
Subs not used: Evtimov, Moussi, McGugan, Coppinger.
Scorers: Sharp 25', Blackstock 90'
Booking: Cohen 44'
Blackpool: Gilks, Crainey, Eardley (Dicko 69'), Evatt, Phillips, Gomes (Grandin 59'), Ince, Taylor-Fletcher, Sylvestre (Delfouneso 69'), Baptiste (c), Osbourne.
Subs not used: Basham, Halstead, Angel, Broadfoot.
Booking: Evatt 63'
Scorers: Grandin 70', Taylor-Fletcher 75'
Referee: Eddie Ilderton