Leicester Tigers agreed to host the game to help their neighbours, but it was league leaders Exeter who took the points, scoring five tries in front of a crowd of 1,216 at the home of the defending Guinness Premiership champions.
Chiefs, backed by travelling supporters in good voice and with former Tigers favourite Matt Cornwell at centre, got off the mark with a penalty from Gareth Steenson and added a converted try from right wing Matthew Jess in the opening five minutes.
Fly-half Tim Taylor kicked the Nottingham points as hooker Simon Alcott and scrum-half Haydn Thomas touched down to give the West Country visitors a 28-6 lead at half-time.
Tries from former Bath openside James Scaysbrook and ex-Northampton prop Chris Budgen stretched the lead in the second half.
Nottingham enjoyed their best spell of territory and possession in the closing quarter of the game but were unable to force the breakthrough their commitment deserved until the last move of the game when Jack Cobden, a graduate of the Tigers Academy, dotted down in the right-hand corner. Replacement David Marshall hit the post with the conversion.