Wood’s 55-ball hundred was Derbyshire’s fastest in List A cricket and the second fastest in all formats for the county.
The 27-year-old smashed 14 fours and three sixes in his 59 ball 109 which propelled Derbyshire to 258 for 6 in a game reduced to 27 overs by heavy rain the previous evening.
Harry Came scored 57, his first List A fifty, and an unlikely target of 259 proved beyond Nottinghamshire who were bowled out for 217 with Brett Hutton scoring 46 from 20 balls and Finn Hudson-Prentice taking 3 for 37.
Wood said: "It means the world to me to be honest, a local lad who has come through the ranks. It's been a long time coming but I think it means even more to get to this stage.
"The atmosphere was brilliant and it's always great to play against Notts and to be able to come out and have a performance and a result like that is all the more pleasing."
Nottinghamshire head coach Peter Moores said: "I think the bowlers would take it on the chin, we didn't bowl well enough. Credit to them, Wood and Came played really well on a really good pitch.
"We've been at Derby plenty of times and seen if you don't get it right you can get hurt. I think ultimately we bowled too many loose balls and they put them away and just got too many."
The start had been delayed by three-and-a-half hours while groundstaff dried out part of the square that was saturated when it was left uncovered overnight.
After matting was eventually used to put over the wet areas, the match began at 2.30pm with Wood and Came going into overdrive after Nottinghamshire elected to bowl.
Although Mitch Wagstaff skied Joey Evison to point, Came pulled Hutton for six and drove Liam Patterson-White over the long off boundary.
Dane Paterson conceded 14 from his third over which also included four byes and Came pulled Evison for his third six before missing a sweep at Patterson-White.
Brooke Guest was bowled advancing at Patterson-White but Wood pulled Hutton for a big six as 18 came from the 20th over.
Alex Hughes was lbw trying to swing a full length ball from Paterson and after Hudson-Prentice lofted Patterson-White over long off for six, he was brilliantly caught by Peter Trego diving full length at mid off.
Wood took three fours from Luke Fletcher and then drove Paterson for six as Nottinghamshire leaked 65 from the last four overs.
His hundred came when he pulled Hutton for his third six and he left to a standing ovation when he was caught at short third man off the last ball of the innings.
It needed something special for Nottinghamshire to deny Derbyshire their first victory in the competition and although Trego briefly threatened to match Wood’s pyrotechnics with 28 from 20 balls, they fell well short.
Trego and Matthew Montgomery added 54 in five overs but an athletic catch by Wagstaff at point removed Montgomery and Trego miscued a pull at George Scrimshaw.
Lyndon James was stumped coming down the pitch to Mattie McKiernan and Nottinghamshire’s fading hopes ended when former Derbyshire batsman Ben Slater drilled Alex Thomson to long off.
Hutton enjoyed himself in the evening sunshine but could not save Nottinghamshire from their first defeat to Derbyshire in one-day cricket since 2004.