Leading at the break thanks to terrific counter-attacking goals from Tahith Chong, Chiedozie Ogbene and Ross Barkley, the Hatters fell apart in the second period.
Dominic Solanke got the Cherries’ first goal five minutes after the restart to pull one back but two goals in the space of two-and-half minutes – from Illia Zabarnyi and Antoine Semenyo – drew the hosts level.
Barkley missed a big chance for the Town to restore their on 71 minutes but with six minutes to go the Cherries led for the first time when Semenyo thundered a shot beyond Thomas Kaminski.
Despite nine minutes of injury time the Hatters couldn’t find a leveller and Bournemouth celebrated a famous comeback.
For the Town, it's back to Kenilworth Road on Saturday for a huge fixture against Nottingham Forest.
See you then.
Town: Kaminski; Kaboré, Doughty, Hashioka (sub Mpanzu 67), Mengi, Burke; Barkley (sub Berry 88), Clark; Chong (sub Woodrow 73), Ogbene (sub Townsend 88), Morris.
Subs not used: Shea, Krul, Nelson, Piesold, Martins.