Former Bristol City star Pitman, 25, rifled in his 19th league goal of the campaign in the 92nd minute for Eddie Howe's men.
Defender Steve Cook headed his first ever goal in Bournemouth colours to open the scoring after 24 minutes after a fine cross from Simon Francis.
Mid-table Carlisle came racing out of the blocks in the second half and captain Lee Miller converted an acrobatic overhead kick from Jon-Paul McGovern's cut back after 50 minutes.
But Carlisle were not level for long. Just five minutes later Harry Arter rifled home past stranded Carlisle goalkeeper Mark Gillespie to nudge Bournemouth back in front.
It was left for Pitman to seal a club record eighth successive win for the south-coast club when he fired left-footed to send the home fans into raptures.