The Lions looked set to secure a fourth win in five league games courtesy of Steve Morison's early header - the striker's fifth goal of the season.
But Blackstock - who blazed a penalty over the bar in the ninth minute - grabbed an equaliser for the hosts with 10 minutes remaining when he rose to convert Chris Cohen's cross.
The goal was no less than Forest deserved after they dominated proceedings for much of the afternoon.
But although Blackstock's goal lifted some of the gloom surrounding the City Ground, Billy Davies' men are still searching for their first victory of the season in all competitions.
Nathan Tyson replaced the injured Paul Anderson (knee) in the only alteration to the Forest line-up.
Millwall boss Kenny Jackett also made one change, with Darren Carter starting in place of Liam Trotter.
Visiting goalkeeper David Forde was forced into action early on to keep out a deflected shot from Robert Earnshaw.
Yet it was Millwall who took the lead in the fifth minute, Morison flashing a header across the face of Lee Camp after Danny Schofield had provided a fine cross from the left.
Forest were handed a golden opportunity to draw level four minutes later when Alan Dunne was penalised for a rash challenge on Tyson inside the area.
However, Blackstock was unable to hit the target with the resulting spot-kick.
Neil Harris came close to doubling Millwall's advantage with an audacious long-range chip, but the back-pedalling Camp tipped his effort over the bar.
The visitors threatened again soon after, Morison heading narrowly over on this occasion following a swift counter-attack.
Forest - who lost Earnshaw to injury in the 27th minute - put Millwall under heavy pressure for the remainder of the half, but lacked a cutting edge in the final third.
And the Lions almost added a second eight minutes before half-time as the lively Morison nodded over from Dunne's centre.
Forest remained on top after the interval and Cohen's deflected free-kick almost caught out Forde.
The Lions keeper then made two fine stops in the space of a minute to deny Wes Morgan before pulling off a stunning triple save to keep out efforts from Radoslaw Majewski, Ryan Bertrand and Tyson.
By this stage, the home fans could have been forgiven for thinking it wasn't their team's day, but the Reds finally drew level when Blackstock beat Forde to head home Cohen's looping cross.
Millwall responded immediately with Carter drilling a shot narrowly wide, while at the other end Forest substitute Anderson lifted a shot over the bar with only the keeper to beat.
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