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."