Sean O'Driscoll's side continued their unbeaten start to the season at Selhurst Park.
The Reds had looked on course for defeat in south London until the 26-year-old squared things up nine minutes from time.
Palace had deservedly taken a 50th-minute lead when Kagisho Dikgacoi, fresh from netting the winner at Charlton on Friday, headed home an Owen Garvan corner.
Forest's task was then made all the more difficult in the 63rd minute when substitute Adlene Guedioura was sent off for foolishly kicking out at Mile Jedinak, although another replacement saved his blushes.
Blackstock saved the day by prodding home eight minutes after coming on for Billy Sharp and would have won the match for Forest but for a superb Julian Speroni save.
Palace had a chance of their own late on as well, but Peter Ramage saw a point-blank effort stopped by Lee Camp.
Coming into the game, Dougie Freedman - fresh from completing a deal for former QPR defender Danny Gabbidon - made three changes against the side he spent two seasons with as a player.
Simon Cox and Dan Harding were the two alterations made by Forest for the south London clash in which both sides started brightly.
Late challenges and awry passing meant it took until for the ninth minute for either side to fashion a clear-cut chance and Glenn Murray could not have come much closer, meeting Wilfred Zaha's right-wing cross with a header that hit the post.
It began a spell of dominance for the hosts, who saw Jonathan Williams test Camp with a driven 20-yard effort and an unbalanced Zaha put over from the same distance.
Dikgacoi attempted his own long-range effort shortly after, before Camp could only unconvincingly parry away a fierce strike from Palace captain Jedinak.
Murray was next to test the Northern Ireland international as, while Palace's attacks became sparser, Forest were struggling to eke out any opportunities of note.
A testing first half for the visitors was made tougher five minutes from the break when Sam Hutchinson went off injured and was replaced by Guedioura.
There was another blow for Forest fives minutes after the restart when Garvan's corner was met by Dikgacoi at the back post, with his header looping into the far corner.
Yannick Bolasie twice came close as the hosts looked to extend their advantage, before Forest saw Guedioura given a straight red card for rashly kicking out at Jedinak.
The hosts received a blow of their own as Dikgacoi went off injured, but they recovered well and saw a Ramage header chalked off for an infringement.
Despite the South African's absence, the hosts were well on top until nine minutes from time when Cox played through substitute Blackstock, who prodded under Speroni to level the scores.
The former Southampton striker would have given Forest a surprise victory had it not been for an excellent save by Palace's Argentinian goalkeeper, before Ramage was impressively denied by Camp at the other end.