Chris Hughton's side's recent form had pushed them up to the fringes of the top two and the loan signings of Erik Huseklepp and Andros Townsend had further bolstered their promotion hopes.
However, Blackstock's opener shortly before the half-hour mark left them with work to do and after Chris Burke (55) had levelled, the striker struck again in the 63rd minute to secure the win for Forest.
Marlon King and Nikola Zigic made a rare start together up front after various injury niggles of late.
King started brightly without forging a chance of note, while Burke and Townsend sent in speculative crosses which were comfortably dealt with by the visitors.
Chris Gunter made progress at the other end while Guy Moussi's shot was blocked and Andy Reid probed from set-pieces.
Birmingham's lacklustre performance was penalised in the 29th minute as Garath McCleary crossed from the right side of the box for Blackstock to react sharply by poking home with his left foot from close range.
Townsend sent in another cross which came to nothing and Reid blazed over for Forest.
Adlene Guedioura fired wide from distance as Forest continued to impress, while Gunter sent in further poor centres from the flanks.
Blues left-back David Murphy's hopeful free-kick from some distance was off target as the half-time whistle approached.
City right-back Jonathan Spector asked questions with crosses from the right before McCleary shot wide of the goal. Reid's free-kick was saved easily by Boaz Myhill before, at the other end, the lively Townsend saw a shot blocked from outside the box.
That spell paid off as Burke then equalised in the 55th minute as King did well on the right, sending the ball inside for the winger to turn home with his left foot.
Less than 10 minutes later Forest were back in front, however. It was the same combination, too, as McCleary found space on the right to send in a teasing ball which Blackstock, left-footed, fired into the top-right of goal from 12 yards.
Huseklepp was sent on for Zigic while Murphy blazed over.
King forced a good parried save from Camp before Nathan Redmond's effort from 25 yards went wide.
Moussi sent one wide at the other end but Birmingham laid siege. Keith Fahey's shot hit the bar with Camp looking beaten and centre-half Curtis Davies sent an effort off target as Hughton's Blues were frustrated.