Blackstock had only been on the pitch eight minutes when he volleyed beneath Blackpool goalkeeper Matt Gilks.
It had looked like Blackpool would take all three points after quickfire strikes from substitute Elliot Grandin and Gary Taylor-Fletcher usurped the lead given to Forest by Billy Sharp's first-half goal.
Tiago Gomes and Ludovic Sylvestre both started for Blackpool as manager Ian Holloway made two changes. The pair came into the side at the expense of Angel Martinez and Nathan Delfouneso, who were named on the bench
Forest made one change with Radoslaw Majewski replacing the suspended Adlene Guedioura. Blackstock was among the substitutes after his ban alongside Jermaine Jenas, who was also back in the squad.
Stephen Crainey threatened for Blackpool early on after a neat one-two with Tom Ince as his shot clipped the outside of a post on its way wide.
Forest felt they should have had a fifth-minute penalty when Chris Cohen went down inside the area under pressure from Isaiah Osbourne but the referee waved away the appeals.
Sharp put Forest ahead after 25 minutes. Blackpool failed to clear their lines from a corner and Danny Collins' shot deflected up into the air before falling to Sharp, who flicked the ball past Gilks from 10 yards out.
It was Blackpool's turn to have protests for a penalty turned down when Daniel Ayala brought down Ince on the half-hour mark.
Forest enjoyed another escape five minutes before half-time when Sylvestre put Taylor-Fletcher through on goal. He took the ball round onrushing goalkeeper Lee Camp but Greg Halford managed to clear the danger.
Andy Reid came close to putting Forest 2-0 ahead when his 64th-minute free-kick whistled narrowly wide.
Blackpool were level after 70 minutes. Matt Phillips was given time and space to cross and Grandin rose unmarked to head home.
And Holloway's team had turned the game around five minutes later.
A scramble in the box was never convincingly cleared by Forest and the ball broke to Taylor-Fletcher, who guided a shot into the bottom corner past the outstretched arm of Camp.
Soon afterwards, only a last-ditch tackle from Halford prevented Delfouneso extending the lead.
Sharp had a glorious chance to equalise when he latched on to Blackstock's flick-on but he mishit his shot when one-on-one.
Forest probably thought that would be their final chance to take something from the game, but when when Cohen's cross was headed back across goal by Simon Cox, Blackstock was on hand to chest the ball down and finish in style.