The striker converted a low centre from Lee Beevers after 23 minutes for his first goal for nine weeks. His shot went in off a post and Bournemouth never looked like retrieving the setback.
Bournemouth might have scored after three minutes when a shot from Lee Bradbury was blocked on the line by goalkeeper Rob Burch.
But the Cherries, still second from bottom, had precious few chances until Jeff Goulding saw a shot in injury time go narrowly wide.
Lincoln should have added further goals but on two occasions Lee Frecklington fired over the bar from the edge of the area.
Imps goalkeeper Burch saved a header from Danny Hollands but there were few other openings in a match of little incident.