Lenell John-Lewis scored the only goal as Lincoln stretched their unbeaten run to seven matches at Bournemouth.
The Cherries almost scored early on when Lee Bradbury's shot was blocked on the line by goalkeeper Rob Burch.
But the home side faded after that and John-Lewis soon put Lincoln ahead when his shot went in off a post.
Lee Frecklington fired over and Danny Hollands had a header saved as Lincoln pressed while Bournemouth's Jeff Goulding shot wide in injury time.
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Booked: Hollands.
Booked: Oakes, Frecklington.
Goals: John-Lewis 24.
Att: 4,464
Ref: Roger East (Wiltshire).
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