Somma, on loan from Leeds, struck in the 82nd minute when he controlled a long ball from Matt Saunders before hitting the back of the net from 30 yards.
Bournemouth, without an away win since early February, dominated for long spells but could not find a way through the Lincoln defence.
Striker Alan Connell had a great chance after 17 minutes but put his shot wide from a good position.
Lincoln made the Cherries pay six minutes later when Chris Herd headed on for Somma to run clear and score an easy goal.
Bournemouth almost levelled in the 25th minute when a powerful shot from leading scorer Brett Pitman was pushed away by Lincoln keeper Rob Burch. Pitman went close again early in the second half when his low shot was blocked by Burch.
But the Cherries finally drew level in the 69th minute when a free-kick from Rhoys Wiggins was bundled home by Pitman for the striker’s 23rd goal of the season only for Somma to strike late on.