The Seasiders will now face West Ham United in the richest game in football at Wembley next week.
Blackpool boss Ian Holloway said: "Words are going to fail me. I'm so proud.
"We got ourselves in a brilliant situation and what a fantastic fightback that was. If they had got the equaliser I could not see us coming back.
"But we're going to Wembley again, it's just magnificent.
"Halfway through the second half I felt fine. Once they got a goal it changed everything. It got the crowd on their side and we forgot to play.
"At the end of the day it was about finishing with one more goal than them and I am very proud of my boys for coming through."