Brave Bath let no-one down but they did not do quite enough to beat a side that have not lost at home for nearly a year.
Jon Callard's men hammered on the door for the whole of the second half but the Newport defence held firm to protect the lead they established with three first-half tries.
The visitors could consider themselves unfortunate to be beaten, especially by an 11-point margin but Newport are a formidable side on their own ground and they were worthy winners.
Bath trailed 22-10 at the end of a pulsating first half.
The Welsh side drew first blood when wing Matt Mostyn burst through the middle and put Matthew Watkins over.
A Jon Preston penalty reduced the deficit but Newport stretched their lead when Mostyn skinned Adedayo Adebayo to go over in the corner.
Bath then played some outstanding rugby as Gareth Cooper went over from a scrum.
However, Newport scored again on the stroke of half-time, hacking on a loose ball from a ruck to leave it 22-10 at the interval.
Shane Howarth's penalty on the hour all but wrapped things and another on the final whistle condemned Bath to defeat.
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