A goal within two minutes helped Kettering to extend Bath City's winless streak to 11 games.
The visitors gained the early advantage through Djoumin Sangare, who stabbed home Jerel Ifil's headed knock-down from close range.
Bath threatened through Ben Swallow but the midfielder saw his effort well saved by goalkeeper Laurie Walker.
Walker was again on hand to deny the hosts deep into stoppage time, saving well from substitute Scott Murray.
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Bath City defender Andy Gallinagh told BBC Radio Bristol:
"We dominated the game and we've conceded a sloppy goal in the first five minutes and we are very disappointed.
"We're all trying to do the right thing and maybe it's just the final ball and we need to be scoring goals.
"We shot ourselves in the foot when we let the goal in."
Kettering Town manager Mark Stimson told BBC Radio Northampton:
"It was a great start to score early on.
"I thought the two boys coming into the team - (John) Dempster and (Ben) Smith were a cut above the rest in quality.
"A centre-half who can header and defend and who has a bit in the locker with the ball and then Ben's energy and ability was fantastic for the 90 minutes."