The league leaders thrashed the bottom side at Bloomfield Road as Eddie Howe's side bounced back from their 3-1 defeat to Liverpool in midweek.
Matt Ritchie had a good opening for Bournemouth, but he scuffed his shot when well placed early on. He soon made amends when he opened the scoring on 18 minutes.
The Bournemouth midfielder struck a fairly tame effort from around 20 yards out, and the ball somehow squirmed past Blackpool goalkeeper Joe Lewis.
Steven Davies fired in a long-range effort for the Seasiders on the half-hour mark, but the effort was comfortably held by Artur Boruc in the Bournemouth goal.
The Championship leaders extended their advantage three minutes before the break when Callum Wilson turned the ball home from around six yards.
The Seasiders had the ball in the net shortly after, but the goal was ruled out for a foul on goalkeeper Boruc as the ball was bundled over the line.
Ritchie then struck his second of the afternoon when he curled home a long-range effort which looked to have taken the wind out of the Blackpool sail on the hour mark.
However, they soon responded courtesy of substitute Delfouneso, before the three-goal advantage was restored almost immediately through Brett Pitman's penalty.