Ben Futcher equalised five minutes later for Lincoln, heading home from a corner, but Bournemouth regained the lead on the stroke of half-time when Carl Fletcher hit home from six yards out after lsoing his marker.
Stephen Purches and Gareth O'Conner extended the lead to 4-1, and although Mark Bailey got another strike for Lincoln the game was killed off when Carl Fletcher headed home his second of the game in the 83rd minute.