The Cherries had looked to be going home with all three points after Steve Fletcher’s 54th-minute header.
It would have been the perfect present for departing boss Eddie Howe, who confirmed after the game that he is set to take over at Burnley.
But Gillespie ruined his night with a double strike in the last 14 minutes.
First, he steered the ball home after a low cross-shot from debutant Ben Coker. Then, seven minutes from time, he showed composure to send a close-range lob over Cherries goalkeeper Shwan Jalal.
Bournemouth thought they had scored a winner after Fletcher rose to header home Liam Feeney’s cross. But it was not to be and Howe’s reign ended in defeat.