Forest were unbeaten at home in 20 games and had not conceded at the City ground in more than 12 hours.
The hosts had the ideal start when Rob Earnshaw’s early strike brought the two teams level on aggregate.
Blackpool were enjoying more of the play but Forest looked dangerous on the break.
But all this changed after the interval when DJ Campbell scored a dramatic second-half hat-trick for Blackpool as the visitor’s showed how to score on the counter attack.
In the 56th minute Blackpool went back in front through Campbell.
Earnshaw scored his second only for Stephen Dobbie’s long-range effort take a huge deflection off Wes Morgan to make it 2-2.
But as Forest pushed forward for a goal Blackpool clinically finished them off on the counter.
Campbell then scored in the 76th and 79th minutes for the first treble of his career.
Dele Adebola fired home a consolation for Forest in stoppage time but it is the Seasiders who are just 90 minutes from returning to the top flight of English football for the first time since 1971.