Goodwin put on 103 for the fifth-wicket with Carl Hopkinson (51) to set up a quarter-final away to Lancashire in English cricket's knockout one-day competition.
Set just 196 to win, Sussex wobbled at the start of their reply before reaching their target with three overs to spare.
South African Johan van der Wath hit the winning runs in style with a straight six off left-arm spinner Samit Patel.
Goodwin, who faced 84 balls, went when he swept off-spinner Graeme Swann and was caught at short fine leg.
Man-of-the-match Hopkinson was out with Sussex 21 runs short of victory when he was bowled by Patel having hit four fours in 79 deliveries.
Sussex lost Ian Ward and Michael Yardy in a dramatic opening over from former Yorkshire seamer Ryan Sidebottom.
Ward was bowled first ball, playing half forward, before Yardy - fresh from his career-best 257 against Bangladesh - also went for a duck, playing no stroke.
Nottinghamshire did well to bat out their 50 overs after collapsing to 12 for three and later 111 for eight.
Patel's maiden One-day fifty helped give Nottinghamshire's bowlers something to defend and the 20-year-old put on 73 for the ninth wicket with Gareth Clough (22).
In the end Patel's 61 off 52 balls featured four sixes and three fours.
Earlier, veteran Nottinghamshire opener Darren Bicknell was lbw to van der Wath for three before Swann was taken at point off James Kirtley.
Jason Gallian was run out and New Zealand captain Stephen Fleming, after adding 67 with David Hussey, went the same way having scored 50 from 58 balls with seven fours and a six.