Tries from debutant Louis Brown, Callum Irvine, Mike Myerscough and Joe Buckle secured the bonus-point.
The home side opened the scoring when a smart offload found Ben Brownlie who crashed over from close range.
Tiff Eden added the extras.
But the Carnegie response was immediate, with Brown crossing on his first appearance for the club after collecting an Alex Davies stab forward.
Davies then kicked the conversion to bring the scores level.
A penalty from Davies then edged the visitors in front.
Nottingham were gifted the lead when a stray pass was intercepted by Jordan Coghlan who had a simple walk over.
Back came Yorkshire and when the hosts were penalised at the breakdown Davies booted the three points from near halfway.
Yorkshire were then penalised at the breakdown and after Nottingham failed to make use of their penalty advantage Eden took the three points.
The home side were then penalised for not rolling away and Davies kicked his third penalty of the half. Carnegie were then reduced to 14 when Pete Lucock was sent to the sin-bin for not releasing near the line. Eden kicked the resulting penalty to put Nottingham four points ahead.
A moment of opportunism from replacement Irvine then gave Carnegie the lead.
Having sold the dummy twice to two Nottingham defenders the ex-Harrogate fly-half crossed under the posts.
Like buses, Yorkshire’s second try of the half came moments later. George Watkins’ slaloming run made ground, allowing Mike Myerscough to barge over from close in.
But the hosts worked the ball wide for Alexander Goble to score with his first touch. Eden’s conversion set up a grandstand finish.
However, Joe Buckle then scored a late try from close range to make sure of the win and secure a try bonus-point.
Nottingham: Scanlon, Robinson, Evans, Lyons, Spittle (Goble 74), Eden, Veenendaal (McConnell 63), West, Brownlie (Stevens 53), Burke (Langley 68), Holmes (Everard 68), Qualter, Coghlan, Poullett (Buckley 53).
Yorkshire Carnegie: Elder, Watkins, Forsyth, Lucock (Irvine 38-40), Brown, Davies (Irvine 66) Green (Homer 63), Thomas (Imiolek 74), Buckle, Beech (Thraves 63), Whetton, Smith, Bainbridge, R. Mayhew (c), Stedman (Myerscough 54).