Adam Cunnington scored for the third successive game as Kettering recorded a win at Forest Green.
James Norwood fired straight at visiting keeper Laurie Walker from long range and Cunnington saw his own shot from distance blocked by Jamie Turley.
Cunnington gave the Poppies the lead shortly after the break when he headed home from Sol Davis' cross.
Norwood had another shot saved by Walker late on as Kettering held out for the win.
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Forest Green manager Dave Hockaday told BBC Radio Gloucestershire:
"I'm not disappointed with the performance, I'm disappointed with the result because we've dominated everything, but then came an individual error.
"We've had loads of chances. We passed them off the park and they'd almost given up, but we haven't put the ball in the back of the net.
"It's not that we're not creating chances, because we're getting the ball in the box, we are getting one on ones, free headers and shots, but we're not scoring goals and that puts pressure on the defence."
Kettering Town manager Mark Stimson told BBC Radio Northampton:
"I thought the performance was honest and hard working, without being too good with the football.
"First and foremost it's about rolling your sleeves up and putting in a performance.
"We kept a clean sheet. The boys defended well. Cunnington's overall work rate was phenomenal."