The Premier League side came from behind to dump Stags out at the third round stage with Christian Saydee striking the decisive blow.
Mansfield had deservedly led 1-0 at the break, but were beaten by goals on 67 and 90 minutes to leave the players, management and Stags fans gutted at the final whistle.
The Stags putting in a dominant performance first half and hit the front through a goal from Noah Stokes after 15 minutes.
They had plenty of other chances to extend that lead, with Tyrese Sinclair in outstanding form, and Jimmy Knowles hitting the underside of the bar.
See who you can pick out in our fans gallery from Mansfield Town v Derby County
Supercomputer predicts the most likely result for Leyton Orient v Mansfield Town, Bradford City v Newport County, Stockport County v Colchester United and every other League Two game
Former Mansfield Town boss Mick Jones dies aged 75
One more new face in for Mansfield Town as early injuries mount?
Mansfield Town boss Nigel Clough proud of players and fans as Stags are pipped by Derby County in Carabao Cup classic
Sinclair won numerous free-kicks with his trickery, and had several impressive shots at goal from distance.
He looked special, and it was easy to see why he was on the bench for the Checkatrade Trophy game against Scunthorpe.
At the other end Stags keeper Keaton Marrs made two fine saves for the Stags in the first half, but Bournemouth created little else.
The second half saw Bournemouth come much more into the game and they were marginally on top when they equalised on 67 minutes from a corner.
After that, Bournemouth were right on top as the Stags players possibly tired.
But it was cruel on the Stags that Bournemouth nicked the winner on the stroke of 90 minutes as Saydee fired into the bottom corner of the net from inside the box.