The Poppies ended Alfreton Town’s nine-match unbeaten run with Callum Stead’s first-half penalty being enough to earn a 1-0 victory in the final home game of the season.
With Gloucester City bagging a late equaliser to draw 1-1 at Boston United, it meant Kettering moved back into the play-off places with just one game to go.
They will head to Curzon Ashton on Saturday ahead of Boston, who travel to Farsley Celtic, by just two goals on goal difference.
A win should be enough unless the Pilgrims can win big at Farsley but, nonetheless, Kettering have things in their own hands.
And Culverhouse insists that in itself is a huge achievement after the Poppies had been fancied to be battling against the drop this season.
“It’s all credit to the group,” the Kettering manager said.
“They have been outstanding since the first day we walked in. They have given everything for the shirt, they really have.
“They were out on their feet. We were on a bus for nine hours, less than 48 hours ago, so to come out and put that amount of effort in again is unbelievable.
“They were outstanding. We rode our luck a bit in the second half when they camped us in a little bit.
“You could see the energy levels were dropping but that dressing-room is buzzing now with the news that Gloucester got the late equaliser.
“To a man, they have been outstanding and they have given us everything.
“Hopefully they get their rewards because they are a credit to be around. They are a really good, young group who are learning all the time but are only going to get better.
“We now go to Curzon with a chance, that’s what we’ve got - a chance.
“But the group have done that, they have put themselves in a magnificent position.
“It’s well documented we were people’s favourites to go down so what they have achieved here is unbelievable.”