Buxton survived a missed penalty from the hosts in the first half before toughing it out after half-time.
“It was an important point,” said the defender. “Everyone can see where we are in the table and what we are trying to do.
“We take the point as a positive and we move forward to next Saturday.
“It was a game of the centre-halves today. We limited them to few chances in the second half.
“It was a bit shaky in the fist and we got lucky with the penalty, but we saw it through.
“Their forward line was physical and let you know they were there, they challenged for everything.
“They are a good team and they know how to play this pitch. It is not our style but we got the job done. You can't be disappointed with a clean sheet though.”
Whitby enjoyed the best of the first half chances with Bradley Fewster being denied by a great Ben Turner tackle on 17 minutes.
Theo Richardson made two crucial saves in the 10 minutes prior to the interval, first saving with his feet from Jacob Hazel and then making a vital blocking save again to deny the ex-Silverlander.
Luck too played a part in the 25th minute when Warren Clarke conceded a penalty, only for Jake Hackett to sky it over the bar.
For the second half Nathan Fox replaced Clarke in an adapted 4-4-2 system, with Diego De Girolamo and Ash Chambers the front pairing.
As Dan Cowan drove forward, Buxton showed renewed purpose in seeking the fluency on the ball that had so far eluded them and from the 57th minute could have been facing 10 men, had the officials been less lenient when Jassem Sukar kicked the grounded Chambers.
The clearest chance of the half on 65 minutes fell to Whitby when Fewster blasted high and wide. That was Whitby's last serious attack as thereafter the Bucks at last began to prosper.
It saw more possession and greater control on the ball, with the industrious Chris Dawson and Lindon Meikle prominent.
Fox dragged a shot wide from 10 yards, before Dan Cowan just missed the target at the death.