Bath remain rooted to the foot of the table as Lincoln picked up only their second home win of the season.
The Imps took the lead when Sam Smith headed home Gavin McCallum's teasing cross from close range.
McCallum turned from provider to scorer when he struck from 12 yards after being set up by Simon Russell.
The visitors' best effort came from Alex Russell, whose right-footed drive was expertly tipped round the post by Lincoln's Joe Anyon.
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Lincoln City manager Steve Tilson told BBC Lincolnshire:
"With them not having won all season everyone expected us to win but no game's an easy one. I'm pleased we got three points and are back up and running again.
"I thought we played really week in the first half, we played some really good stuff and went 2-0 up.
"The second half was a bit dreary, we didn't get the ball down and play as much as I would have liked but we got the job done."
Lincoln City 01 Anyon 03 Nutter 05 Gowling 06 Hone 13 Sinclair 08 Power 10 Fuseini (O'Keefe - 75' ) 15 Russell 27 Christophe 30 McCallum (Barraclough - 75' ) 14 Smith (Perry - 90' ) Substitutes 04 Watts 17 Nicolau 23 O'Keefe 09 Perry 19 Barraclough Bath City 01 Garner 05 Jones 19 Burnell (Stonehouse - 60' ) 24 Clough 26 Gallinagh Booked 11 Hogg 16 Canham 18 Watkins (Murray - 54' ) 21 Russell 10 Phillips (Canham - 38' ) 23 Swallow Substitutes 04 Rollo 15 Preece 03 Stonehouse 07 Murray 27 Canham
Ref: Seb Stockbridge