Tom Ince’s 44th-minute strike was the only goal of the game.
Seasiders boss Ian Holloway admitted he had his heart in his mouth.
He said: “If they had got an equaliser then, I would have been absolutely fuming.
“We were terrific, probably deserved to be further ahead.
“I asked my boys for a big performance and that’s what they gave me.
“Can we do it again? It will be one heck of an achievement if we do and it’s set up to be another great evening. There was bit of luck about the goal — but we created four clear-cut chances to their one.”