The superb victory at the City Ground helped the Seasiders to a 6-4 victory on aggregate which left the home side broken hearted.
Billy Davies' side had finished third in the table but that counted for little as Ian Holloway's side sent their fans into dreamland.
It took only seven minutes for Forest to level the scores on aggregate as Robert Earnshaw pounced in trademark fashion.
Radoslaw Majewski sent a pass through the centre and, after Nottingham-born defender Alex John-Baptiste had failed to intercept, the striker took full advantage by slotting an accurate finish inside the post to sent the City Ground into raptures.
John-Baptiste made amends as Forest continued to pressure, sliding in with a vital challenge to block Earnshaw's shot after the Wales international had initially pulled clear of the visiting defence again.
Blackpool had threatened early on with a spectacular, dipping volley from Brett Ormerod that dropped only narrowly wide of goal.
And as their confidence grew, Charlie Adam - the player who had netted in all three previous clashes between these two sides this season - came close himself in equally impressive fashion when his vicious strike from the edge of the box wasacrobatically palmed over the bar by Lee Camp.
Forest responded with a low, skimming shot from Chris Cohen that, although he didn't seem to properly connect with, still flew inches wide of the post.
While another flowing, swift flurry of passes saw Dexter Blackstock dance into the box but fire straight at a grateful Matt Gilks.
Blackpool were enjoying the larger share of possession as the half drew to a close but without carving out the chances to reflect that.
Forest fans were on their feet again early in the second half after Blackstock rolled a pass down the centre for Earnshaw, who again finished with aplomb only for the celebrations to be cut short by a tight looking offside flag.
The atmosphere was suddenly muted, however, as Blackpool hit Forest on the counter-attack to bag a vital goal with Campbell the calmest man on the City Ground pitch as he lifted a composed finish over the advancing Camp after being picked out by Gary Taylor-Fletcher's precise pass.
Forest seemed to see the confidence dented but Blackstock came close with a header and then Earnshaw struck for a second time to lift the roof off the City Ground again.
This time there was no offside flag as Blackstock brought the ball down in the box and Earnshaw pounced to fire home high into the net from six yards.
But Forest's joy was shortlived as Blackpool struck again to put themselves back in the driving seat.
Substitute Stephen Dobbie was the hero, although he enjoyed a huge slice of luck as his shot took a massive deflection off Cohen to leave Camp helpless and steer it into the net.
Still Forest refused to give up and Nathan Tyson's pace down the left gave him the room to cross to the near post where Blackstock forced an outstanding save from Gilks at close range, with the keeper regaining his feet to then deny Earnshaw.
But Campbell then struck twice in the space of two minutes to settle the tie once and for all.
Firstly he bent an unstoppable shot beyond Camp after exchanging passes with Dobbie and then as he picked up the pieces after Dobbie's close-range shot had been saved.
Dele Adebola pulled one back for the home side in injury time but it was not enough to deny Blackpool their place at Wembley.