Sam Allardyce's side triumphed 1-0 as a Benni McCarthy saw a free-kick delivery into the box - which looked to be more cross than shot - arc over everyone and high into the net in the 37th minute.
But despite dominating for long periods, this was a night when Forest just couldn't find the back of the net with Jason Brown's penalty save from Blackstock in the 73rd minute the most wasteful moment.
Forest had paid the price for missed chances against Blackpool in the Championship on Saturday and the theme was continued in painful fashion against the Premier League side.
The home side almost entirely dominated the first half hour, but still ended up going into the interval behind.
Blackstock bundled an instant shot straight into the arms of keeper Brown early on following a powerful header across goal from Joe Garner.
Blackburn skipper Ryan Nelsen produced a goal-saving tackle to deny Robert Earnshaw after the little striker had instantly controlled a fine cross from Nathan Tyson on the edge of the six-yard box.
Defender Wes Morgan lashed badly wide when a Chris Cohen cross was only half cleared to him ten yards out.
And Tyson, who was so often the creator down the left flank, flashed a shot narrowly the wrong side of the upright himself after being picked out by Joel Lynch.
Even after McCarthy's strike it was Forest who were pressing and Earnshaw's spectacular 20-yard free-kick bounced back off the bar and away to safety.
The second half began in more even fashion but it was still the home side who looked the more likely to score as Lynch and Chris Gunter delivered telling crosses from the opposing flanks, with Nelsen producing another timely interception to deny Earnshaw a chance.
Blackburn came close to adding a second as Nikola Kalinic showed a flash of quality with a smart turn and shot that flashed narrowly wide.
Forest missed the best chance of all to level when they were awarded a penalty when Steven Reid handled in the box.
However, Brown plunged low to his left to palm away Blackstock's spot-kick in the 73rd minute to book his side's passage into the fourth round.